**Acknowledgements**

I acknowledge Dr. Dietmar Appelhans (Leibniz Institute of Polymer Research Dresden, Dresden, Germany) for the generation of histidine-maltose PPI dendrimers, collaboration, and valuable discussions.

The work is supported by MultiPark (Lund University), Vinnova, Swedish Research Council grants.


*3.4. Effectiveness of Doll Therapy on Behaviour*

Four out of seven studies [20,29,30,32] reported a reduction in SCPD, observing the decrease of disruptive and aggressive behaviors. The participants were less agitated and irritable while holding the doll (Cantarella Mdiff: −0.025, *p* < 0.001; Shin: *t* = 16.31, *p* < 0.01; Balzotti *z* = 2.66, *p* < 0.007). They verbalized fewer swear words, fewer shouts, and fewer obsessive behaviors. Three studies [20,30,32] found a higher number of interactions with the environment, increasing social contact and verbalization (*t* = −8.41, *p* < 0.01). The episodes of erratic wandering decreased in two of the studies (Shin, *t*: −17.46, *p* < 0.001) [20,33]. Only one study [29] did not report significant evidence in reducing anxiety, agitation, and aggressiveness (Moyle, *p* < 0.88)


*7.4. Salinity*

Although approximately 5% of the earth's wastewaters are extremely saline, MFC may be more helpful in treating these wastewaters. Increased salinity improves power generation through increased conductivity. Increased conductivity promotes proton transport and therefore reduces the system's internal resistance. Lefebvre et al. demonstrated that adding up to 20 g/L of NaCl improved the cumulative efficiency of MFCs by decreasing internal resistance by 33% and boosting maximum power output by 30% [154].


**Polymer/pressurizing fluid interactions**

The isobaric temperature-controlled scanning transitiometry (*T*CST) (Grolier et al., 2004; Bessières et al., 2005) is used to investigate the phase changes via the Clapeyron's equation while the pressure is transmitted by various fluids. The enthalpy, volume and entropy

Thermodynamics and Thermokinetics to Model Phase Transitions of Polymers

**100 nm**

24 hrs in vacuum.)

**Modulation of the decorative particles distribution**

cylinders by grafted polar groups (Watanabe et al., 2007).

**25nm**

**(a) (b)**

Fig. 4. Pattern control in the nanometric scale of PEO-*b*-PMA(Az) under multifaceted *T, P,* CO2 constraints with AuNPs. TEM illustrations of BC on carbone coated copper grid **(a)** PEO114-*b*-PMA(Az)46, **(b)** PEO454-*b*-PMA(Az)155 doped with AuNPs under SCCO2 (9 MPa, 353 K). Black spots are AuNPs wetted hexagonal PEO honeycomb, selectively. PEO is **(a)** 8.6, **(b)** 24.3 nm in diameter with a periodicity of **(a)** 17.1, **(b)** 36.6 nm. (Step 1, BC film preparation before modification: 2 wt% toluene solution solvent-casting, annealing at 423 K for 24 hrs in vacuum. Step 2, AuNPs deposition before modification: droplet of an ethanol solution of hydrophilic AuNPs (solvent in toluene of 1 %) on dried BC film, drying at r.t. for 2 hrs.)

**(a) (b) (c ) (d)**

**PMA(Az) PEO**

**Substrate**

Fig. 3. Pattern control in the nanometric scale under multifaceted *T, P* and CO2 constraints, 2 hrs annealed. AFM phase, tapping mode, illustrations on silicon substrate **(a)** neat PEO114-*b*-PMA(Az)46, PEO 'softer' than PMA(Az) appears brighter (whiter), **(b)** GCO2 saturation (5 MPa, r.t.), **(c)** LCO2 saturation (9 MPa, r.t.), PMA(Az) surrounding PEO becomes 'softer', **(d)** SCCO2 saturation (9 MPa, 353 K), PEO becomes 'softer' while swelling. Inserts **(b-c-d)** are schematic representations of CO2-induced changes of PEO cylinders. (BC film preparation before modification: 2 wt% toluene solution spin-coating, 2000 rpm, annealing at 423 K for

To create nano-scale hybrid of metal-polymer composites, the favourable SCCO2/PEO interactions are advantageously exploited, as illustrated in **Fig. 4.a-b**. They enable a tidy pattern of hydrophilic gold nano-particles (AuNPs). AuNPs are of about 3 nm in diameter and stabilized with thiol end-functional groups (Boal & Rotello, 2000). Preferentially, the metal NPs wet one of the two copolymer domains, the PEO channels, but de-wet the other, the PMA(Az) matrix. This requires a high mobility contrast between the two copolymer domains, heightened by CO2 plasticization that enhances the free volume disparity between copolymer parts. Each SCCO2-swollen PEO hydrophilic hexagonal honeycomb allows the metal NPs to cluster. A two-dimensional (2D) periodic arrangement of hydrophilic AuNPs is generated in the organic PEO in turn confined into smectic C phase of PMA(Az) matrix which has potential molecular mobility. Additionally to the plasticizing action, the force of the trap is driving chemically. It is due to the hydrophilic compatibility of AuNPs in PEO

over Extended Temperature and Pressure Ranges Under Various Hydrostatic Fluids 653

**Substrate PEO PMA(Az)**

**Substrate**

**PMA(Az) PEO**

**50nm**

changes are quantified *versus* the (high) pressure of either Hg, CO2, or N2 (Yamada et al., 2007a-b). The hydrostatic effect of "more or less chemically active" solvent CO2, or N2 is smaller than the hydrostatic effect of mercury. The adsorbed solvent induces smaller volume changes at the isotropic transition than the mercury pressure. This results from the low compressibility of solvent (gas) molecules compared to the free volume compressibility induced in BC. A particular behaviour is observed with "chemically active" CO2 where the quadrupole-dipole interactions favour the CO2 sorption into the PMA(Az) matrix during the isotropic liquid transition (Kamiya et al., 1998; Vogt et al., 2003). The hydrostatic effect by CO2 overcomes above 40 MPa with a CO2 desorption at higher pressures explained by the large change of molecular motions at the isotropic transition upon the disruption of πbounds with azobenzene moieties.

### **Modulation of the surface topology and swelling of the CO2-modified nanometric-phaseseparated organization**

Supercritical carbon dioxide (SCCO2) constitutes an excellent agent of microphase separation. From *ex-situ* Atomic Force Microscopy (AFM) and Transmission Electron Microscopy (TEM) analysis of the pattern organization, the fine control of the pressure together with the temperature at which the CO2 treatment is achieved demonstrates the possibility to modulate the surface topology inversion between the copolymer phases concomitantly with the swelling of the nano-phase-separated organization. The observed phase contrast results from the coupled effect of the different elastic moduli of the two domains of the block-copolymer with chemo-diffuso phenomenology.

Remarkably, the preferential CO2 affinity is associated with the thermodynamic state of CO2, from liquid (9 MPa, room temperarture (r.t.)) to supercritical (9 MPa, 353 K) and then to gaseous (5 MPa, r.t.) state (Glasser, 2002). This is typically observed when annealing the copolymer for 2 hours to keep the dense periodic hexagonal honeycomb array **(Fig. 3.a-d)**. Under gaseous CO2, the surface morphology of PEO cylinders is not significantly expanded **(Fig. 3.a-b)**. However, liquid CO2 induces a first drastic shift at the surface with the emergence of a new surface state of PEO cylinders. This surface state inversion is attributed to domain-selective surface disorganization. PMA(Az) in the glassy smectic C (SmC) phase cannot expand. PEO cylinders dissolve favourably within liquid CO2, with polar interactions, get molecular movement, expand preferentially perpendicularly to the surface substrate **(Fig. 3.c)**. By increasing temperature, liquid CO2 changes to supercritical CO2. The PMA(Az) domain is in the SmC phase and get potential molecular mobility. At this stage, the copolymer chains should be easily swelled. The easiness of SCCO2 to dissolve within liquid PEO cylinders deals with a new drastic change of the surface topology where the absorbed SCCO2 increases the diameter of the PEO nano-tubes **(Fig. 3.d)**.

The preferential CO2 affinities produce porous membranes with a selective sorption in hydrophilic semicrystalline 'closed loop', *i.e.*, PEO channels (Boyer et al., 2006a). More especially, under supercritical SCCO2, the PEO cylinders kept in the ordered hexagonal display exhibit the highest expansion in diameter. In the case of PEO114-*b*-PMA(Az)46, the exposure to SCCO2 swells the PEO cylinders by 56 %, with arrays from 11.8 nm in diameter at r.t. to 18.4 nm in diameter at 353 K. The lattice of the PMA matrix, *i.e.*, periodic plane distance between PEO cylinders, slightly increases by 26 %, from 19.8 nm at r.t. to 24.9 nm at 353 K. This microphase separation is driven by disparity in free volumes between dissimilar segments of the polymer chain, as described from the entropic nature of the closed-loop miscibility gap (Lavery et al., 2006; Yamada et al., 2007a-b).

Fig. 3. Pattern control in the nanometric scale under multifaceted *T, P* and CO2 constraints, 2 hrs annealed. AFM phase, tapping mode, illustrations on silicon substrate **(a)** neat PEO114-*b*-PMA(Az)46, PEO 'softer' than PMA(Az) appears brighter (whiter), **(b)** GCO2 saturation (5 MPa, r.t.), **(c)** LCO2 saturation (9 MPa, r.t.), PMA(Az) surrounding PEO becomes 'softer', **(d)** SCCO2 saturation (9 MPa, 353 K), PEO becomes 'softer' while swelling. Inserts **(b-c-d)** are schematic representations of CO2-induced changes of PEO cylinders. (BC film preparation before modification: 2 wt% toluene solution spin-coating, 2000 rpm, annealing at 423 K for 24 hrs in vacuum.)


**3. Percutaneous therapies for tricuspid regurgitation in heart failure**

#### **3.1. Functional tricuspid regurgitation**

Functional tricuspid regurgitation (TR) represents over 90% of cases of TR and it is typically due to tricuspid annular dilatation (mainly in anteroposterior diameter) and right ventricular (RV) enlargement (leading to leaflet tethering) secondary to progressive left heart disease (LHD) [86]. The tricuspid valve (TV) has been considered for years the "forgotten" valve. This issue may be explained by the fact that TR was believed to be well tolerated and reduced after treating LHD. On the contrary, patients with significant TR and HF tend to be highly symptomatic due to decrease in CO and abdominal and peripheral congestion [87]. Furthermore, the presence of moderate or severe TR is independently associated with an increased mortality (over 25% at 1 year) regardless of biventricular function or pulmonary pressures [88, 89].

Despite surgical treatment of LHD, significant TR can be found in over two-thirds of patients in long-term follow-up, suggesting that a lower threshold for TV repair should be considered when MV surgery is carried out [87, 90–92]. Current data support that TV repair at the time of MV surgery is safe, whereas reoperation for persistent TR is related to high morbidity and mortality rates [93–95]. Notwithstanding, few patients undergo TR surgery and the vast majority are managed medically. Data from the STS database suggest that moderate to severe TR is present in almost 2 million of patients in the United States, but not even 10,000 undergo TV surgery each year. Progressive RV dysfunction may lead to an irreversible RV damage, which is thought to be the reason for the poor outcomes of late surgery in this scenario. Therefore, there is a large unmet clinical need for patients with significant TR who are not referred for conventional surgery, mainly due to expected high-surgical risk. Percutaneous therapies for functional TR are emerging as an alternative to surgery in this scenario. Patients with symptomatic severe TR and prior open-heart surgery and those with significant TR and progressive RV dysfunction and failure despite OMT may benefit from transcatheter TV interventions. Initial experiences include the off-label use MV devices and first-in-human cases of dedicated new technologies [96] (**Table 4**). Among different therapies that have been tested in preclinical setting, transcatheter TV annuloplasty, resembling different successful surgical techniques, might be one of the most promising approaches [97, 98].

#### **3.2. Transcatheter tricuspid valve interventions**

#### *3.2.1. Percutaneous tricuspid valve repair with mitral valve dedicated devices*

The acquired experience in catheter-based therapies for MV with satisfactory results has emerged the appealing concept of using some of these devices in tricuspid position. Recently, Braun et al. have reported first series of edge-to-edge TV repair in 18 patients with moderate to severe functional TR and right-sided heart failure [99]. Six patients were treated for isolated severe TR, whereas 12 patients were treated concomitantly to PMVR. A reduction of at least one TR grade was achieved in all patients and no in-hospital major events were reported. A significant improvement in TR was observed (TR ≥ 3+ 94% vs. 33%, *p* < 0.001) and sixteen patients (89%) referred an improvement in NYHA functional class at 30-day follow-up. In 2015, the first-in-human transcatheter TV repair with Mitralign® system was published, reproducing Kay posterior annuloplasty [100]. Recently, acute results of Trialign® early human use were reported. A single pair of pledgets was successfully implanted in 14 of the 16 patients (87.5%), with an average postprocedural reduction of 37% in TA and 59% in TV regurgitant orifice area. No procedural mortality occurred. Potential advantage of additional pledgets will be assessed. Cardioband® has been also successfully implanted in TA in humans [101] and European CE mark study (TRI-REPAIR) is currently initiated.

#### Percutaneous Treatment of Mitral and Tricuspid Regurgitation in Heart Failure http://dx.doi.org/10.5772/intechopen.68493 129

**Table 4.** Catheter-based therapies for TR that have been already tested in humans.

issue may be explained by the fact that TR was believed to be well tolerated and reduced after treating LHD. On the contrary, patients with significant TR and HF tend to be highly symptomatic due to decrease in CO and abdominal and peripheral congestion [87]. Furthermore, the presence of moderate or severe TR is independently associated with an increased mortality (over 25% at 1 year) regardless of biventricular function or pulmonary pressures [88, 89]. Despite surgical treatment of LHD, significant TR can be found in over two-thirds of patients in long-term follow-up, suggesting that a lower threshold for TV repair should be considered when MV surgery is carried out [87, 90–92]. Current data support that TV repair at the time of MV surgery is safe, whereas reoperation for persistent TR is related to high morbidity and mortality rates [93–95]. Notwithstanding, few patients undergo TR surgery and the vast majority are managed medically. Data from the STS database suggest that moderate to severe TR is present in almost 2 million of patients in the United States, but not even 10,000 undergo TV surgery each year. Progressive RV dysfunction may lead to an irreversible RV damage, which is thought to be the reason for the poor outcomes of late surgery in this scenario. Therefore, there is a large unmet clinical need for patients with significant TR who are not referred for conventional surgery, mainly due to expected high-surgical risk. Percutaneous therapies for functional TR are emerging as an alternative to surgery in this scenario. Patients with symptomatic severe TR and prior open-heart surgery and those with significant TR and progressive RV dysfunction and failure despite OMT may benefit from transcatheter TV interventions. Initial experiences include the off-label use MV devices and first-in-human cases of dedicated new technologies [96] (**Table 4**). Among different therapies that have been tested in preclinical setting, transcatheter TV annuloplasty, resembling different successful surgical

techniques, might be one of the most promising approaches [97, 98].

*3.2.1. Percutaneous tricuspid valve repair with mitral valve dedicated devices*

and European CE mark study (TRI-REPAIR) is currently initiated.

The acquired experience in catheter-based therapies for MV with satisfactory results has emerged the appealing concept of using some of these devices in tricuspid position. Recently, Braun et al. have reported first series of edge-to-edge TV repair in 18 patients with moderate to severe functional TR and right-sided heart failure [99]. Six patients were treated for isolated severe TR, whereas 12 patients were treated concomitantly to PMVR. A reduction of at least one TR grade was achieved in all patients and no in-hospital major events were reported. A significant improvement in TR was observed (TR ≥ 3+ 94% vs. 33%, *p* < 0.001) and sixteen patients (89%) referred an improvement in NYHA functional class at 30-day follow-up. In 2015, the first-in-human transcatheter TV repair with Mitralign® system was published, reproducing Kay posterior annuloplasty [100]. Recently, acute results of Trialign® early human use were reported. A single pair of pledgets was successfully implanted in 14 of the 16 patients (87.5%), with an average postprocedural reduction of 37% in TA and 59% in TV regurgitant orifice area. No procedural mortality occurred. Potential advantage of additional pledgets will be assessed. Cardioband® has been also successfully implanted in TA in humans [101]

**3.2. Transcatheter tricuspid valve interventions**

128 Interventional Cardiology

#### *3.2.2. Transcatheter tricuspid valve repair therapies*

TriCinch® (4Tech Cardio, Galway, Ireland) consists of a steerable catheter with a corkscrew at the tip. Under echocardiographic and fluoroscopic guidance, supraannular fixation of the device is carried out in the mid part of the anterior TA. Afterwards, the catheter is tensioned in order to produce TA cinching, therefore reducing the anteroseptal dimension of the TA and improving leaflet coaptation. Finally, a self-expandable nitinol stent is positioned at the inferior vena cava in order to secure the system and maintain the tension applied. TriCinch® implantation preserves the native anatomy, allowing potential future treatment options. First in-human cases [102, 103] and early results from the PREVENT CE trial have been reported. The system was successfully implanted in 13 of 18 patients (72%). Two patients developed periprocedural hemopericardium and device TA detachment was observed in two patients. No mortality events occurred during up to 29 months follow-up. A significant improvement in 6-minute walk test and quality of life were documented, although only 37.5% remain in NYHA class I–II during this period.

#### *3.2.3. Other percutaneous approaches for tricuspid regurgitation*

The FORMA® Repair System (Edwards Lifescience, Irvine, USA) is a valve spacer created to increase coaptation surface by occupying space in the regurgitant orifice of the TV. The device is usually delivered through a transsubclavian venous route and anchored to the RV apex distally and proximally fixed within a small surgically prepared pocket. Preliminary results in seven high-risk patients with severe TR and advanced NYHA functional class III–IV were recently available [104]. The device was successfully implanted in all patients without major complications, obtaining at least one grade acute reduction in TR. 30-day results showed clinical improvements (100% NYHA class II) and stable TR reduction (100% moderate TR) without significant tricuspid stenosis.


*3.2. Instruments*

The Portuguese middle version of COPSOQ II [20] was used to assess the psychosocial factors among all the teachers using the Portuguese curriculum. The questionnaire was applied in international schools. Teachers could be of different nationalities and they had knowledge of the British curriculum.

Psychosocial risk analysis was performed using questionnaires on the Google Forms platform to ensure data confidentiality. In response to the questionnaires, respondents responded privately. These answers were not disclosed to the hierarchical superiors of the educational establishment.

National and international public and private schools participated in the study, namely:

The selected schools are essentially dedicated to preparing students for the completion of secondary education and conducting exams for access to university education. These schools began their activities in different decades, but they all have the objective of promoting the academic success of their students in common. Emphasis was given to the number of students admitted to universities. It was decided that only teachers from the 3rd cycle and secondary education (teachers with students aged between 13 and 18 years old) would be studied at the school. This choice was based on the fact the tasks performed by this group of workers are exposed to greater psychosocial risks as they deal with a group of students with an average of 25 students during school periods.

The questionnaire was applied online, following a previous contact given the informed consent by the teachers. *The Copenhagen Psychosocial Questionnaire II* (COPSOQ II) was sent via email to be completed, which could be done on computers on the school premises or at home. These results were stored in the Google forms database.

The items of COPSOQ II are measured using a five-point Likert scale, and the results of the scales can be presented from one to five points or transformed using the cutting points of 2.33 and 3.66 in order to obtain a traffic light graphic [20].

The variables measured on a Likert scale were analyzed through the presented categories, while the quantitative variables were analyzed from the measured values, such as the average obtained for each question (for questions on a scale of 1 to 5, a value greater than 3 is greater than the midpoint of the scale), the standard deviation associated with each question representing the absolute dispersion of responses, the coefficient of variation illustrating the relative dispersion of responses, the minimum and maximum values observed for the answers given to the various questions. An internal consistency analysis was also carried out, allowing the study of the properties of measurement scales and the questions that integrate them. Cronbach's Alpha is the most used model in the social sciences for checking scales' internal consistency and validity, measuring how a set of variables represent a given dimension. An internal consistency coefficient value measured by Cronbach's Alpha greater than 0.80 is considered adequate, and an internal consistency coefficient between 0.60 and 0.80 is considered acceptable. Statistical tests used in this study serve to ascertain whether the differences observed in the sample are statistically significant, that is, whether the conclusions of the sample can be inferred for the population. The value of 5% is a reference value used in Social Sciences to test hypotheses; it means that we establish the inference with an error probability of less than 5%. As the sample size is in these conditions, it will not be necessary to verify the assumption and parametric tests can be applied. As the groups under study can be considered significant, the parametric Student's *t*-test is used to analyze a quantitative variable in both classes of a dichotomous qualitative variable to verify the significance of the differences between the means observed for both the groups of the dichotomous variable. The t-test poses the following hypotheses:

When the test value of the t-test is greater than 5%, the null hypothesis is accepted. That is, there are no differences between the two groups. The null hypothesis is rejected when the test value is less than 5%. Therefore, there are differences between the two groups. The use of the chi-square test is addressed; in the face of two nominal variables or a nominal and an ordinal variable, the appropriate test to verify the relationship between each pair of variables is the chi-square, in which we have the hypotheses:

The null hypothesis is rejected when the test value is less than 5% (0.05), concluding that the two variables are related. When the test value is greater than the 5% reference value, we cannot reject the null hypothesis that the two variables are independent; it is concluded that they are unrelated.


*Article* **Causality and Renormalization in Finite-Time-Path Out-of-Equilibrium** *φ***3 QFT**

**Ivan Dadi´c 1 and Dubravko Klabuˇcar 2,\***

Received: 30 November 2018; Accepted: 9 January 2019; Published: 18 January 2019

**Abstract:** Our aim is to contribute to quantum field theory (QFT) formalisms useful for descriptions of short time phenomena, dominant especially in heavy ion collisions. We formulate out-of-equilibrium QFT within the finite-time-path formalism (FTP) and renormalization theory (RT). The potential conflict of FTP and RT is investigated in *gφ*3 QFT, by using the retarded/advanced (*R*/*A*) basis of Green functions and dimensional renormalization (DR). For example, vertices immediately after (in time) divergent self-energy loops do not conserve energy, as integrals diverge. We "repair" them, while keeping *d* < 4, to obtain energy conservation at those vertices. Already in the S-matrix theory, the renormalized, finite part of Feynman self-energy Σ*F*(*p*0) does not vanish when |*p*0| → ∞ and cannot be split to retarded and advanced parts. In the Glaser–Epstein approach, the causality is repaired in the composite object *GF*(*p*0)Σ*F*(*p*0). In the FTP approach, after repairing the vertices, the corresponding composite objects are *GR*(*p*0)Σ*R*(*p*0) and Σ*A*(*p*0)*GA*(*p*0). In the limit *d* → 4, one obtains causal QFT. The tadpole contribution splits into diverging and finite parts. The diverging, constant component is eliminated by the renormalization condition 0|*φ*|0 = 0 of the S-matrix theory. The finite, oscillating energy-nonconserving tadpole contributions vanish in the limit *t* → ∞.

**Keywords:** out-of-equilibrium quantum field theory; dimensional renormalization; finite-time-path formalism

#### **1. Introduction and Survey**

In many regions of physics, the interacting processes are embedded in a medium and require a short-time description. To respond to such demands, neither vacuum S-matrix field theory [1–5], nor equilibrium QFT [6–16] with the Keldysh-time-path [17–28] suffice. The features, a short time after the beginning of evolution, where uncertainty relations do not keep energy conserved, are to be treated with the finite-time-path method. Such an approach includes many specific features that are not yet completely understood. A particular problem, almost untreated, is handling of UV divergences of the QFT as seen at finite time. The present paper is devoted to this problem. We consider it in the simplest form of *λφ*3 QFT, but many of the discussed features will find their analogs in more advanced QED and QCD.

Starting with perturbation expansion in the coordinate space, one performs the Wigner transform and uses the Wick theorem. The propagators, originally appearing in matrix representation, are linearly connected to the Keldysh base with *R, A*, and *K* components. For a finite-time-path, the lowest order propagators and one-loop self-energies taken at *t* = ∞ correspond to Keldysh-time-path propagators and one-loop self-energies. For simplicity, the label "∞" is systematically omitted throughout the paper, except in the Appendix with technical details.

To analyze the vertices, one further separates *K*-component [27,28] into its retarded (*K,R*) and advanced (*K,A*) parts:

$$G\_{R}(p) = G\_{A}(-p) = \frac{-i}{p^{2} - m^{2} + 2ip\_{0}\epsilon},$$

$$G\_{K}(p) = 2\pi\delta(p^{2} - m^{2})[1 + 2f(\omega\_{p})]$$

$$\omega\_{p} = G\_{K,R}(p) - G\_{K,A}(p),$$

$$G\_{K,R}(p) = -G\_{K,A}(-p) = h(p\_{0}, \omega\_{p})G\_{R}(p),$$

$$\omega\_{p} = \sqrt{\vec{p}^{2} + m^{2}}, \quad h(p\_{0}, \omega\_{p}) = -\frac{p\_{0}}{\omega\_{p}}\left[1 + 2f(\omega\_{p})\right].\tag{1}$$

Matrix propagators are (*i* and *j* take the values 1, 2):

$$\mathcal{G}\_{\vec{l}\vec{\jmath}}(p) = \frac{1}{2} [\mathcal{G}\_K(p) + (-1)^{\vec{l}} \mathcal{G}\_R(p) + (-1)^{\vec{l}} \mathcal{G}\_A(p)]. \tag{2}$$

Specifically:

$$\mathcal{G}\_{\mathbb{F}}(p) = \mathcal{G}\_{11}(p)\_{f(\omega\_p) = 0} = \frac{-i}{p^2 - m^2 + 2i\epsilon'} \, \mathcal{G}\_{\mathbb{F}}(p) = -\mathcal{G}\_{\mathbb{F}}^\*(p). \tag{3}$$

#### **2. Results**

#### *2.1. Conservation and Non-Conservation of Energy at Vertices*

Having done all this, one obtains the vertex function (for simplicity, all the four-momenta are arranged to be incoming to the vertex). For the simplicity of discussion, all the times corresponding to the external vertices (*j*) of the whole diagram are assumed equal (*x*0,*j*,*ext* = *t*, all *j*; otherwise, some factors, oscillating with time, but inessential for our discussion, would appear), so that the vertex function becomes:

$$\frac{i}{2\pi} \frac{e^{-it\sum\_{i} p\_{0i}}}{\sum\_{i} p\_{0i} + i\epsilon}. \tag{4}$$

This expression [27–29] integrated over some *dpo*,*k* by closing the time-path from below gives the expected energy conserving *δ*(∑*i p*0*i*), with the oscillating factor reduced to one. If the integration path catches additional singularity, say the propagator's *D*(*pk*) pole at *p*¯0*k*, for this contribution, conservation of energy is "spoiled" by a finite amount Δ*E* = ∑ *i p*0*i* + *p*¯0*k*, and there is an oscillating vertex function (*i*/2*π*)*e*−*it*Δ*E*/(Δ*E* + *i* ). Note: the fact that some time is lower or higher than another, i.e., *t*1 > *t*2 or *t*1 < *t*2, survives Wigner transform in the character of ordering (retarded or advanced) of the two-point function.

In general, we have the following possibilities:

• If the vertex time is lower than the other times of all incoming propagators, there are additional contributions, and energy is not conserved at this vertex. The oscillations are just what we would expect from the Heisenberg uncertainty relations. It is how the time dependence emerges in the finite-time-path out-of-equilibrium QFT. The ill-defined pinching singularities—products of retarded and advanced propagators with the same (*p*0,*p*), only partially eliminated for the Keldysh time-path [30]—do not appear here as the propagator energies *p*0 and *p* 0 are different variables, so that the singularities do not coincide except at the point *p*0 = *p* 0. Thus, the pertinent mathematical expressions are well defined.

In the *λφ*3 QFT, there are two divergent subdiagrams: the tadpole diagram and self-energy diagram, considered separately in the following subsections.

#### *2.2. UV Divergence at the Tadpole Subdiagram*

In the perturbation expansion, the tadpole diagram (Figure 1) appears as a propagator with both ends attached to the same vertex, which is the (lower-time) end-point vertex of the second propagator.

The tadpole subdiagram without a leg is simple. Of the three components, the loop integral vanishes for the *R* and *A* components and diverges for the *K*, *R* and *K*, *A* ones. At finite *κ* = 4 − *d*, these integrals are real constants related to the *F* and *F*¯ components. In the limit *d* = 4, the renormalization performed on *F* and *F*¯ makes them finite.

$$\begin{split} &ig\boldsymbol{\mu}^{\kappa/2} \frac{\int d^d p}{(2\pi)^d} \mathcal{G}\_R(p) = ig\boldsymbol{\mu}^{\kappa/2} \frac{\int d^d p}{(2\pi)^d} \mathcal{G}\_A(p) = 0, \\ &\mathcal{G}\_{\text{Tad}} \equiv -ig \frac{\int d^d p}{(2\pi)^d} \mathcal{G}\_{K,A}(p) = -ig\boldsymbol{\mu}^{\kappa/2} \frac{\int d^d p}{(2\pi)^d} \frac{p\_0}{p^2 - m^2 - 2ip\_0\varepsilon} = ig\boldsymbol{\mu}^{\kappa/2} \frac{\int d^d p}{(2\pi)^d} \mathcal{G}\_{K,R}(p), \\ &\Longrightarrow -\frac{1}{2} \mathcal{G}\_{\text{Tad}} = -\frac{ig\boldsymbol{m}^2}{8\pi^2\kappa} - \frac{ig\boldsymbol{m}^2}{16\pi^2} [1 - \gamma\_\varepsilon + \ln(\frac{4\pi\mu^2}{m^2})] + \mathcal{O}(\kappa) + ig \frac{\int d^3 p}{(2\pi)^3} 2f(\omega\_p) \\ &= -\frac{ig\boldsymbol{m}^2}{8\pi^2(\kappa)} + finite \text{vacuum term} + finite \, f(\omega\_p) \text{ term.} \end{split} \tag{5}$$

(Above, and throughout the paper, *γE* denotes the Euler-Mascheroni constant, *γE* ≈ 0.5772.)

For a tadpole subdiagram with a leg (see Figure 1), we have two vertices; higher in time (*t*2), which is the connection to the rest of the diagram, and lower in time (*t*1, *t*1 < *t*2) with the tadpole loop. The lower vertex does not conserve energy.

One has to add contributions from vertices of Type 1 and Type 2. We write it symbolically with the help of the Wigner transform, the connection between the Keldysh-time-path propagators and the finite-time-path propagators at the time *t* = ∞ and transition to the *R*/*A* basis. The derivation given in the Appendix A shows that:

$$\mathcal{G}\_{\text{tail},\text{j}}(\mathbf{x}\_2) = -\mathcal{G}\_A(0,0)\mathcal{G}\_{\text{Tad}} + \int \frac{dp\_{02}}{2\pi} \frac{i e^{ip\_{02}\mathbf{x}\_{02}}}{p\_{02} - i\varepsilon} [\mathcal{G}\_A(p\_{02}, 0) - \mathcal{G}\_A(0,0)] \mathcal{G}\_{\text{Tad}}\,. \tag{6}$$

The contribution is split into the first, energy-conserving term, and the second term, oscillating with time, in which energy is not conserved at the vertex 1 [31].

The tadpole counterterm follows the same pattern:

$$\mathcal{G}\_{\text{count},\text{j}}^{\text{tadpole}}(\mathbf{x}\_{2}) = -G\_{A}(0,0) + \int \frac{dp\_{02}}{2\pi} \frac{i e^{ip\_{02}\mathbf{x}\_{02}}}{p\_{02} - i\epsilon} \left[ G\_{A}(p\_{02}, 0) - G\_{A}(0, 0) \right]. \tag{7}$$

Notice the similarity of the expressions (6) and (7).

An important point here is that the tadpole contribution splits into two: (1) the energy-conserving part and (2) the energy nonconserving part.

In the energy conserving part, the constant multiplying the counterterm may be adjusted to satisfy the renormalization condition 0|*φ*|0 = 0 of the S-matrix theory, by which the tadpoles are completely eliminated from perturbation expansion. Nevertheless, the terms proportional to *f* survive. The energy nonconserving terms oscillate with time, with the frequency depending on the energy increment. In the competition with the contributions of subdiagram without tadpoles, they fade with time, thus giving the same *t* → ∞ limit as expected from S-matrix theory.

The *g*3 order tadpoles and tadpoles with the resummed loop propagator (obtainable after renormalizing the self-energy; see further in the text) do not change our conclusions.

**Figure 1.** The tadpole diagram with a leg.

#### *2.3. UV Divergence at the Self-Energy Subdiagram*

While in the S-matrix theory, there is only Feynman (Σ1 *F*(*p*0,*p*)) one-loop self energy, which does not depend on the frame, in out-of-equilibrium FT, we have self-energies Σ1 *R*(*p*0,*p*), Σ1 *A*(*p*0,*p*), and Σ1 *K*(*p*0,*p*), which is frame dependent through *f*(*ωp*) (notice here that we distinguish the "true" retarded and advanced functions from those that carry index *R* (*A*), but do not vanish for *t*2 > *t*1 (*t*2 < *t*1), except at *d* < 4).

$$\Sigma\_R^1(p\_0, \vec{p}) = -i\mathfrak{g}^2 \mu^\kappa \int \frac{d^d q}{2(2\pi)^d} [G\_R(p\_0 - q\_0, \vec{p} - \vec{q}) G\_{K,R}(q\_0, \vec{q})]$$

$$\Xi\_{K,R}(p\_0 - q\_0, \vec{p} - \vec{q}) G\_R(q\_0, \vec{q})] = \Sigma\_A^{1,\*}(p\_0, \vec{p}),$$

$$\Sigma\_K^1(p\_0, \vec{p}) = -\Sigma\_{K,R}^1(p\_0, \vec{p}) + \Sigma\_{K,A}^1(p\_0, \vec{p})\tag{8}$$

$$\Sigma\_{\mathcal{K},\mathcal{R}}^{1}(p\_{0\prime}\vec{p}) = -i\,g^{2}\,\mu^{\mathrm{x}}\int \frac{d^{d}q}{2(2\pi)^{d}} \left[\mathcal{G}\_{\mathcal{K},\mathcal{R}}(p\_{0} - q\_{0\prime}\vec{p} - \vec{q})\mathcal{G}\_{\mathcal{K},\mathcal{R}}(q\_{0\prime}\vec{q})\right]$$

$$+\mathcal{G}\_{\mathcal{R}}(p\_{0} - q\_{0\prime}\vec{p} - \vec{q})q\_{\prime}\mathcal{G}\_{\mathcal{R}}(q\_{0\prime}\vec{q})\right] = -\Sigma\_{\mathcal{K},\mathcal{A}}^{1,\*}(p\_{0\prime}\vec{p}).\tag{9}$$

Now, all the integrals containing *f*(*ωp*) are UV finite owing to the assumed UV cut-off in the definition of *f* . Vacuum contributions to Σ1 *K*,*R* are finite separately at *d* → 4; at *d* → 6, this is no longer the case, but their sum is finite.

For retarded and advanced self-energies, imaginary parts and parts proportional to *f*(*ωp*) are UV finite and could be calculated directly from (8). Real, vacuum parts of Σ1 *R* are connected to Σ1 *F*, and we use the results already available from S-matrix renormalization. The connection is:

$$
\Sigma\_{j,k}^1 = \frac{1}{2} \left[ -\Sigma\_{K,R}^1 + \Sigma\_{K,A}^1 - (-1)^k \Sigma\_R^1 - (-1)^j \Sigma\_A^1 \right],
$$

$$
Rc\Sigma\_{R,f=0}^1 = Rc\Sigma\_{11}^1 + \Sigma\_{K,R,f=0}^1 = \Sigma\_F^1 + \Sigma\_{K,R,f=0}^1. \tag{10}
$$

The regularization procedure (either by making *d* < 4 or by introducing fictive massive particles as in Pauli–Villars regularization) is usually considered artificial. Nevertheless, there are efforts to generate necessary massive particles (virtual wormholes) dynamically [32].

For Σ1 *F*(*p*), we find in the literature [33]:

$$\Sigma\_{F}^{1}(p) = \frac{1}{2} 2^{2} g^{2} \frac{\int d^{4}q\_{1} d^{4}q\_{2}}{(2\pi)^{8}} G\_{F}(q\_{1})G\_{F}(q\_{2})(2\pi)^{4} \delta^{(4)}(q\_{1} - q\_{2} - p),$$

$$= \frac{1}{2} g^{2} \frac{\int d^{4}q\_{1} d^{4}q\_{2}}{(2\pi)^{8}} \frac{(2\pi)^{4} \delta^{(4)}(q\_{1} - q\_{2} - p)}{(q\_{1}^{2} - m^{2} + i\epsilon)(q\_{2}^{2} - m^{2} + i\epsilon)},$$

$$\implies \frac{1}{2} g^{2}(\mu)^{\kappa} \int\_{0}^{1} dz \int \frac{d^{4}q'}{(2\pi)^{d}} \frac{1}{[q'^{2} - m^{2} + p^{2}z(1 - z) + i\epsilon]^{2}},$$

$$= \frac{ig^{2}}{32\pi^{2}} (\mu^{2})^{\kappa/2} \Gamma(\kappa/2) \int\_{0}^{1} dz [\frac{p^{2}z(1 - z) - m^{2} + i\epsilon}{4\pi\mu^{2}}]^{-\kappa/2}.\tag{11}$$

The last relation above is still causal. It is UV finite, and it allows the separation into the sum of the retarded and advanced term. However, the expansion of [*p*2*z*(1 − *z*) − *m*2 + *i* /4*πμ*2] −*κ*/2 in power series of |*κ*| is allowed only when *κ* ln[*p*2/(4*πμ*)] << 1; thus, it is a "low energy" expansion, and in spite of the fact that *κ* may be taken arbitrarily small, the limit |*p*0| → ∞ is never allowed.

$$\Sigma\_F^1(p) \approx \frac{ig^2\mu^\kappa}{16\pi^2(\kappa)} - \frac{ig^2\mu^\kappa}{32\pi^2} [\gamma\_\varepsilon + \int\_0^1 dz \ln[\frac{p^2z(1-z) - m^2 + i\varepsilon}{4\pi\mu^2}] ]$$

$$= \frac{ig^2\mu^\kappa}{16\pi^2(\kappa)} + finite. \tag{12}$$

This expression is no longer causal; it is valid only if *κ* ln[*p*2/(4*πμ*)] << 1. One needs the vanishing of self-energy for |*p*0| → ∞, i.e., the region where the opposite condition *κ* ln[*p*2/(4*πμ*)] >> 1 is fulfilled. Then, |Σ1 ∞,*F*(*p*)| → 0 as |*p*0| → ∞ as far as *κ* = 0.

The integration over *z* gives:

$$\Sigma\_{\mathbb{F}}^{1}(p) = -\frac{g^2}{16\pi^2} \left\{ \frac{1}{\kappa} - \frac{\gamma\_\varepsilon}{2} + 1 + \frac{1}{2} \ln(4\pi \frac{\mu^2}{m^2}) - \frac{1}{2} \sqrt{1 - \frac{4m^2}{p^2 + i\epsilon}} \ln \left[ \frac{\sqrt{1 - \frac{4m^2}{p^2 + i\epsilon}} + 1}{\sqrt{1 - \frac{4m^2}{p^2 + i\epsilon}} - 1} \right] \right\} \tag{13}$$

with a high *p*0 limit:

$$\Sigma\_F(p^2, m^2)\_{p^2 \to \infty} \approx -\frac{g^2}{16\pi^2} \left\{ \frac{1}{\kappa} - \frac{\gamma\_E}{2} + 1 + \frac{1}{2} \ln(4\pi \frac{\mu^2}{m^2}) - \frac{1}{2} \ln\left[ -\frac{m^2}{p^2} \right] \right\}.\tag{14}$$

To verify the causality of the two-point function, one may try to project out the retarded part of the finite (subtracted) part of Σ1 *F*(*p*), namely −*i dp* 0 2*π* Σ1 *F*, *finite*(*p*)/(*p*0 − *p* 0 − *i* ), by integration *dp*0 over a large semicircle. However, the contribution over a very large semicircle does not vanish, and the integral is ill defined.

Indeed, we have started from the expressions for *GF* (Σ*F*) containing only retarded and advanced functions, and in the absence of divergence, we expect this to be the truth at the end of calculation. Instead, the function in the last two lines of Expression (12) is not a combination of the *R* and *A* functions, otherwise it should vanish when |*p*0| → ∞ and *κ* are chosen as arbitrarily small; such a behavior can be shifted to an arbitrarily high scale. However, the limit *κ* → 0 remains always out of reach. To preserve causality, we should keep the whole *p*0 complex plane. Specifically, we need the region with large |*p*0|, to be able to integrate over a large semicircle in the complex *p*0 plane, at least to get *dp*0Σ1 *R*(*p*)*GK*,*A*(*p*0) = 0. Thus, we have obtained a result correct at *κ* = 0 and problematic at *d* = 4.

Fortunately enough, there is a way to "repair" causality: the composite object *GF*(*p*)Σ1 *F*(*p*) is vanishing when |*p*0| → ∞; it can be split into its retarded and advanced parts; thus, it is causal. This sort of reparation of causality is possible in other QFT in which logarithmic UV divergence appears. It is similar to the Glaser–Epstein [34–36] approach, where not just Σ, but *G*Σ are the subjects of expansion.

In this spirit, we agree with the conclusion of [37–39]: "Our amplitudes are manifestly causal, by which we mean that the source and detector are always linked by a connected chain of retarded propagators."

Similar is the problem we can see by considering *λφ*4 theory. In this theory, the loop of Figure 2 is a vertex diagram, and the above Glaser–Epstein philosophy does not apply. Nevertheless, the propagator attached to the vertex depends on *p*0 and "improves" the convergence of *dp*0 integration.

**Figure 2.** The vertex diagram.

#### *2.4. Self-Energy Diagram with Legs*

To be able to introduce composite objects with Σ*R*(*A*), we need one of Σ*R*(*A*)'s vertices to conserve energy. The lower in time vertex may be the minimal time vertex, so it does not help in all cases. However, the higher in time vertex would do it, if both the integrals *dq*0 and *dp*0 converge.

The Σ*ij* self-energy contributions with legs (see Figure 2) are:

$$
\begin{array}{cccc}
\ G\_R \Sigma\_{K,R}^1 \ast \ G\_{A\prime} & \mathcal{G}\_R \ast \Sigma\_{K,A}^1 \mathcal{G}\_{A\prime} & \mathcal{G}\_R \Sigma\_R^1 \ast \mathcal{G}\_{K,A\prime} & \mathcal{G}\_{K,R} \ast \Sigma\_A^1 \mathcal{G}\_{A\prime} \\\\ \mathcal{G}\_R \Sigma\_R^1 \ast \mathcal{G}\_{A\prime} & \mathcal{G}\_A \Sigma\_A^1 \mathcal{G}\_{A\prime} & \mathcal{G}\_R \Sigma\_R^1 \mathcal{G}\_{K,R\prime} & \mathcal{G}\_{K,A} \Sigma\_A^1 \mathcal{G}\_A \\\\ \end{array}
\tag{15}
$$

In the above expression, Σs are introduced in Equation (8). "∗" indicates the convolution product, which includes the energy nonconserving vertex. Terms containing Σ1 *K*,*R* and Σ1 *K*,*A* are UV-finite, creating no problems. The other terms, containing Σ1 *R* and Σ1 *A*, are finite as long as *d* < 4, and we may obtain their real part through (11).

Two features seem potentially suspicious: (1) UV divergence in the loop defining Σ1 *R*(*A*) , (2) the ill-defined vertex function between *GR* and Σ1 *R* and between Σ1 *A* and *GA*.

Nevertheless, both problems are resolved at *d* < 4: "to be" UV divergence is subtracted and energy conservation is recovered in the above-mentioned vertices. The composite objects *GR*(*p*)Σ1 *R*(*p*) and Σ1 *A*(*p*)*GFA*(*p*) are now well defined.

#### **3. Discussion and Conclusions**

We examined renormalization prescriptions for the finite-time-path out-of-equilibrium *λφ*3 QFT in the basis of *GR*, *GA*, *GK*,*R*, and *GK*,*A* propagators.

As expected, the number of counterterms did not change, and the formalism enables term by term finite perturbation calculation.

There are some interesting features:

The procedure is therefore generalized for application to more realistic theories (QED and QCD, electro-weak QFT, etc.) by the following:

(A) regularize; (B) do energy-conserving integrals; (C) subtract "to be" UV infinities; (D) deregularize (do limit *d* → 4).

Again, the above described Features (1) and (2) will emerge.

This work contains many of the features [40] arising in the more realistic theories like QED or QCD. Such finite-time-path renormalization is a necessary prerequisite for the calculation of damping rates, and other transition coefficients under the more realistic conditions truly away from equilibrium as opposed to the results obtained within the linear response approximation.

Our plan is to extend the exposed methods to the case of QED. Specifically, we resolve the controversy of the UV diverging number of direct photons in the lowest order of quark QED, as calculated by Boyanovsky and collaborators [41,42] and criticized by [43]. We find that, at the considered one-loop order of perturbation, it is only the vacuum-polarization diagram contributing. The renormalization leaves only finite contributions to the photon production [44].

**Author Contributions:** Conceptualization, I.D. and D.K.; Formal analysis, I.D.; Investigation, I.D. and D.K.; Methodology, I.D. and D.K.; Validation, I.D. and D.K.; Visualization, D.K.; Writing—original draft, I.D.; Writing—review & editing, I.D. and D.K.

**Funding:** This work was supported in part by the Croatian Science Foundation under Project Number 8799 and by STSMgrants from COST Actions CA15213 THORand CA16214 PHAROS.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**

The following abbreviations are used in this manuscript:

#### **Appendix**

This Appendix provides the derivation of Equation (6).

The tadpole diagram, Figure 1, appears as a propagator with both ends attached to the same vertex. We start in coordinate representation. To sum contributions from the vertices of Types 1 and 2, we write the propagators with the help of the Wigner transform. Keldysh-time-path propagators and the finite-time propagators become identical in the limit *t* → ∞. To translate to the *R*/*A* basis, we use *Gi*,*j* = 1 2 [*GK* + (−1)*j GR* + (−1)*i GA*].

*Gtad*,*j*(*x*2) = *igμκ*/2 *ddx*1 ×[*G*1,1(*x*1, *x*1)*G*1,*j*(*x*1, *x*2) − *G*2,2(*x*1, *x*1)*G*2,*j*(*x*1, *x*2)], = *igμκ*/2 *dd*−1*x*1 ∞ 0 *dx*01*e* −*ip*2(*x*1−*x*2) *dd p*1 (2*π*)*d dd p*2 (2*π*)*d* ×[*G*1,1,*x*01 (*p*1)*G*1,*j*,*t*(*p*2) − *G*2,2,*x*01 (*p*1)*G*2,*j*,*t*(*p*2)], *t* = *x*01 + *x*02 2 , = *igμκ*/2 *dd*−1*x*1 ∞ 0 *dx*01 *dd p*1 (2*π*)*d dd p*2 (2*π*)*d* ×*e* −*ip*2(*x*1−*x*2) *dp* 01*dp* 02*Px*01 (*p*01, *p* 01)*Pt*(*p*02, *p* 02) ×[*G*1,1,∞(*p* 1)*G*1,*j*,∞(*p* 2) − *G*2,2,∞(*p* 1)*G*2,*j*,∞(*p* 2)], *p* 1 = (*p* 01,*p*1), *p* 2 = (*p* 02,*p*2), (A1)

where we have used the projection operator *P* connecting time-dependent lowest order propagators with time-independent lowest order propagators [27,28]:

$$\begin{split} G\_{t}(p\_{0},\vec{p}) &= \int\_{-\infty}^{\infty} dp'\_{0} P\_{t}(p\_{0},p'\_{0}) \mathbb{G}\_{\infty}(p'\_{0},\vec{p}),\\ P\_{t}(p\_{0},p'\_{0}) &= \frac{\Theta(t)}{2\pi} \int\_{-2t}^{2t} ds\_{0} e^{i s\_{0}(p\_{0}-p'\_{0})} = \frac{\Theta(t)}{\pi} \frac{\sin 2(p\_{0}-p'\_{0})t}{(p\_{0}-p'\_{0})},\\ \lim\_{t \to \infty} \Pr\_{t \to \infty} \Pr(p\_{0},p'\_{0}) &= \delta(p\_{0}-p'\_{0}),\\ \int\_{-\infty}^{\infty} dp\_{0} e^{-i s\_{0}p\_{0}} P\_{t}(p\_{0},p'\_{0}) &= e^{-i s\_{0}p'\_{0}} \Theta(t) \Theta(2t-s\_{0}) \Theta(2t+s\_{0}). \end{split} \tag{A2}$$

Here, *G* is a bare propagator (matrix propagator or *R*, *A*, or *K* propagator.) A similar relation holds for lowest order self-energies:

$$
\Sigma\_t^1(p\_{0\prime}\vec{p}) = \int\_{-\infty}^{\infty} dp\_0' P\_t(p\_{0\prime}, p\_0') \Sigma\_\infty^1(p\_{0\prime}'\vec{p}),\tag{A.3}
$$

where Σ1 *t* is the retarded, advanced, or Keldysh self-energy.

By using the above relations, we obtain:

*Gtad*,*j*(*x*2) = *igμκ*/2 *dd*−1*x*1 ∞ 0 *dx*01*e* −*ip* 2(*x*1−*x*2) *dd p* 1 (2*π*)*d dd p* 2 (2*π*)*d* ×[*G*1,1,∞(*p* 1)*G*1,*j*,∞(*p* 2) − *G*2,2,∞(*p* 1)*G*2,*j*,∞(*p* 2)], = *igμκ*/2(2*π*)−1 −*i p* 02 − *i δ*(*d*−1) (*p* 2)*e ip* 02*x*02 *dd p* 1 (2*π*)*d dd p* 2 ×[*G*1,1,∞(*p* 1)*G*1,*j*,∞(*p* 2) − *G*2,2,∞(*p* 1)*G*2,*j*,∞(*p* 2)], = *igμκ*/2(2*π*)−1 −*i p* 02 − *i δ*(*d*−1) (*p* 2)*e ip* 02*x*02 *dd p* 1 (2*π*)*d dd p* 2 ×1 2 [−*GK*,∞(*p* 1)*GA*,∞(*p* 2) − *GR*,∞(*p* 1)*GK*,∞(*p* 2) − *GA*,∞(*p* 1)*GK*,∞(*p* 2) +(−1)*j GR*,∞(*p* 1)*GR*,∞(*p* 2)+(−1)*j GA*,∞(*p* 1)*GR*,∞(*p* 2)], (A4)

By taking the fact that tadpoles with *GR* and *GA* vanish, we obtain:

$$\begin{split} G\_{\mathrm{tad},j}(\mathbf{x}\_{2}) &= i g \mu^{\mathbf{x}/2} \frac{(2\pi)^{-1}}{2} \int \frac{i}{p\_{02}^{\prime} - i\epsilon} \delta^{(d-1)}(\vec{p}\_{2}^{\prime}) e^{i p\_{02}^{\prime} \mathbf{x} \mathbf{q} \mathbf{z}} \\ &\times \frac{d^{d} p\_{1}^{\prime}}{(2\pi)^{d}} d^{d} p\_{2}^{\prime} G\_{\mathrm{K},\infty}(p\_{1}^{\prime}) G\_{\mathrm{A},\infty}(p\_{2}^{\prime}), \\ &= (2\pi)^{-1} \int \frac{i}{p\_{02}^{\prime} - i\epsilon} e^{i p\_{02}^{\prime} \mathbf{x}\_{02}} G\_{\mathrm{A},\infty}(p\_{02}^{\prime}, 0) d p\_{02}^{\prime} G\_{\mathrm{Tad}} \\ &G\_{\mathrm{Tad}} = \frac{i g \mu^{\mathbf{x}/2}}{2} \int G\_{\mathrm{K},\infty}(p\_{1}^{\prime}) \frac{d^{d} p\_{1}^{\prime}}{(2\pi)^{d}}. \end{split} \tag{45}$$

Thus,

$$\mathcal{G}\_{\rm tad,j}(\mathbf{x}\_2) = -\mathcal{G}\_{A,\infty}(0,0)\mathcal{G}\_{\rm Tab} + \int \frac{dp'\_{02}}{2\pi} \frac{i\varepsilon^{ip'\_{02}\,\mathbf{x}\alpha}}{p'\_{02} - i\varepsilon} [\mathcal{G}\_{A,\infty}(p'\_{02}, 0) - \mathcal{G}\_{A,\infty}(0,0)]\mathcal{G}\_{\rm Tab}.\tag{A6}$$

The contribution is split into the first, energy-conserving term, and the second term, oscillating with time, in which energy is not conserved at the vertex 1.

#### **References**

c 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **NA61/SHINE Experiment—Program beyond 2020**

#### **Ludwik Turko for the NA61/SHINE Collaboration**

Institute of Theoretical Physics, University of Wroclaw, pl. M. Borna 9, 50-205 Wroclaw, Poland<EMAIL_ADDRESS>Tel.: +48-71-375-9355

Received: 29 October 2018; Accepted: 26 November 2018; Published: 30 November 2018

**Abstract:** The fixed-target NA61/SHINE experiment (SPS CERN) looks for the critical point (CP) of strongly interacting matter and the properties of the onset of deconfinement. It is a scan of measurements of particle spectra and fluctuations in proton–proton, proton–nucleus, and nucleus– nucleus interactions as a function of collision energy and system size. This gives unique possibilities to researching critical properties of the dense hot hadronic matter created in the collision process. New measurements and their objectives, related to the third stage of the experiment after 2020, are presented and discussed here.

**Keywords:** QCD matter; phase transition; critical point

#### **1. Introduction**

The NA61/SHINE, **S**uper Proton Synchrotron (SPS) **H**eavy **I**on and **N**eutrino **E**xperiment, is the continuation and extension of the NA49 [1,2] measurements of hadron and nuclear fragment production properties in fixed-target reactions induced by hadron and ion beams. It has used a similar experimental fixed-target setup as NA49 (Figure 1), but with an extended research program. Beyond an enhanced strong interactions program, there are the measurements of hadron production for neutrino and cosmic ray experiments realized. NA61/SHINE is a collaboration, with about 150 physicists, 33 institutions, and 14 countries being involved.

The strong interaction program of NA61/SHINE is devoted to studying the onset of deconfinement and search for the critical point (CP) of hadronic matter, related to the phase transition between hadron gas (HG) and quark-gluon plasma (QGP). The first order phase boundary between the HG and QGP phase is expected to end at the CP, as seen in Figure 2. At the CP, the sharp first-order phase transition turns into a rapid crossover, resulting in the appearance of large fluctuations of various observables, which are sensitive to the vicinity of the CP. The CP has long been predicted for thermal quantum chromodynamics (QCD) at finite *μB*/*T* [3–5]. Lattice QCD calculations, which are becoming more and more accurate, have led to the present conclusions that the cross-over region occurs at *Tc*(*μB* = 0) = 154 ± 9 MeV [6] and the location of the CP is not expected for *μB*/*T* 2 and *T*/*Tc*(*μB* = 0) > 0.9 [7]. A more detailed exploration of the QCD phase diagram would need both new experimental data with extended detection capabilities and improved theoretical models [8].

The NA49 experiment studied hadron production in Pb + Pb interactions, while the NA61/SHINE collects data varying collision energy (13A–158A GeV) and the size of the colliding systems, as shown in Figure 3. This is, in a sense, equivalent to the two-dimensional scan of the NA61/SHINE piece of the hadronic phase diagram in the (*T*, *μB*) plane, as depicted in Figure 2. Changes in the collision energy lead to different values of the net baryon number chemical potential *μB* and temperature *T*. Different sizes of colliding systems allow to identify the minimum hadronic volume, which can be excited to the state where statistical physics concepts of HG/QGP phase transition are still meaningful. The research program was initiated in 2009, with thep+p collisions used later on as reference measurements for heavy-ion collisions.

**Figure 1.** The present NA61/SHINE detector consists of a large acceptance hadron spectrometer, followed by a set of six Time Projection Chambers (TPCs), as well as time-of-flight (ToF) detectors. The high resolution forward calorimeter, the projectile spectator detector (PSD), measures energy flow around the beam direction. For hadron–nucleus interactions, the collision volume is determined by counting the low momentum particles emitted from the nuclear target with the low momentum particle detector (a small TPC) surrounding the target. An array of beam detectors identifies beam particles, secondary hadrons, and nuclei, as well as primary nuclei, and measures precisely their trajectories.

**Figure 2.** Phase structure of hadronic matter covered by NA61/SHINE (green), compared to present and future heavy ion experiments.

**Figure 3.** For the program on strong interactions NA61/SHINE scans in the system size and beam momentum. In the plot, the recorded data are indicated in green and the approved future data in red.

Hadron production measurements for neutrino experiments are just reference measurements of p+C interactions for the T2K experiment, since they are necessary for computing initial neutrino fluxes at J-PARC. These measurements have been extended to the production of charged pions and kaons in interactions with thin carbon targets and replicas of the T2K target, to test accelerator neutrino beams [9]. The collection of data began in 2007.

Collected p + C data also allow to better understand nuclear cascades in the cosmic air showers—necessary in the Pierre Auger and KASCADE experiments [10,11]. These are reference measurements of p + C, p + p, *π* + C, and K + C interactions for cosmic ray physics. The cosmic ray collisions with the Earth's atmosphere produce air shower secondary radiation. Some of the particles produced in such collisions subsequently decay into muons, which are able to reach the surface of the Earth. Cosmic ray induced muon production would allow to reproduce primary cosmic ray composition if the related hadronic interactions are known [12].

As seen in Figure 2, the phase structure of hadronic matter is involved. Progress in the theoretical understanding of the subject and collecting more experimental data will allow to delve into the subject. While the highest energies achieved at LHC and RHIC colliders provide data related to the crossover HG/QGP regions, the SPS fixed-target NA61/SHINE experiment is particularly suited to explore the phase transition line HG/QGP with the CP included.

#### *Results of Initial NA61/SHINE Research*

The production properties of light and medium mass hadrons, in particular pions and kaons, have been measured [13] according to the NA61/SHINE proposal [1]. The Be + Be results are close to p+p independently of collision energy. Moreover, the data show a jump between light (p + p, Be + Be) and intermediate, heavy (Ar + Sc, Pb + Pb) systems [14]. The observed rapid change of hadron production properties that starts when moving from Be + Be to Ar + Sc collisions can be interpreted as the beginning of the creation of large clusters of strongly interacting matter—the onset of fireball. One notes that non-equilibrium clusters produced in p + p and Be + Be collisions seem to have similar properties at all beam momenta studied here.

The *K*+/*π*+ ratio inp+p interactions is below the predictions of statistical models. However, the ratio in central Pb + Pb collisions is close to statistical model predictions for large volume systems [15].

In p + p interactions, and thus also in Be + Be collisions, multiplicity fluctuations are larger than predicted by statistical models. However, they are close to statistical model predictions for large volume systems in central Ar + Sc and Pb + Pb collisions [16].

The two-dimensional scan conducted by NA61/SHINE by varying collision energy and nuclear mass number of colliding nuclei indicates four domains of hadron production separated by two thresholds: The onset of deconfinement and the onset of fireball [17]. The sketch presented in Figure 4 illustrates this preliminary conclusion. Collected Ar + Sc and Xe + La data are being analyzed to provide further information.

**Figure 4.** The onset of deconfinement and the onset of fireball. The onset of deconfinement is well established in central Pb + Pb (Au + Au) collisions. Its presence in collisions of low mass nuclei, inelastic p + p interactions in particular, is questionable.

Total production cross-sections and total inelastic cross-sections for reactions *π*++C,Al and *K*++C,Al at 60 GeV/c and *π*++C,Al at 31 GeV/c were measured. These measurements are a key ingredient for neutrino flux prediction from the reinteractions of secondary hadrons in current and future accelerator-based long-baseline neutrino experiments [18].

#### **2. New Measurements Requested**

The third stage of the experiment, starting after the Long Shutdown 2 (LS-2) of the CERN accelerator system, would include:

The proposed measurements and analysis are requested by heavy ion, cosmic ray, and neutrino communities. A careful analysis of fluctuations and intermittency phenomena in NA61/SHINE data collected so far is necessary to look for the CP [19].

The objective of **charm hadron production measurements** in Pb + Pb collisions is to obtain the first data on the mean number of *cc*¯ pairs produced in the full phase space in heavy ion collisions. Moreover, further new results on the collision energy and system size dependence will be provided. This will help to answer the questions about the mechanism of open charm production, about the relation between the onset of deconfinement and open charm production, and about the behavior of *J*/*ψ* in quark-gluon plasma.

The objective of **nuclear fragmentation cross-section measurements** is to provide high-precision data needed for the interpretation of results from current-generation cosmic ray experiments. The proposed measurements are of crucial importance to extract the characteristics of the diffuse propagation of cosmic rays in the Galaxy.

The objectives of **new hadron production measurements for neutrino physics** are to further improve the precision of hadron production measurements for the currently used T2K replica target, to perform measurements for a new target material, both for T2K-II and Hyper-Kamiokande experiments, and to study the possibility of measurements at low incoming beam momenta (below 12 GeV/c), relevant for improved predictions of both atmospheric and accelerator neutrino fluxes.

NA61/SHINE is the only experiment which will conduct such measurements in the near future. Together with other HIC experiments, it creates a full-tone physical picture of QCD in dense medium. Especially concerning the strong interaction heavy-ion program, the NA61/SHINE has unique capabilities in comparison with the other experiments (see Figure 2):

The limitations of other experiments are related to: (i) Limited acceptance, (ii) measurement of open charm not considered in the current program, or (iii) very low cross-section at SIS-100.

Concerning other experiments' capabilities shown at Figure 5:

**Figure 5.** Recent (red) and future (green) heavy ion facilities in the phase diagram of strongly interacting matter.

The beam momentum range provided to NA61/SHINE by the SPS and the H2 beam line is highly important for the heavy ion, neutrino, and cosmic ray communities. It covers:

#### *Specific Research Goals*

The NA61/SHINE charm program addresses questions about the validity and the limits of statistical and dynamical models of high energy collisions in the new domain of quark mass, *mc* ≈ 1300 MeV *TC* ≈ 150 MeV [33]. To answer these questions, knowledge is needed on the mean number of charm–anticharm quark pairs *cc*¯ produced in the full phase space of heavy ion collisions.

Such data do not exist yet and NA61/SHINE aims to provide them within the coming years. The related preparations have started already. In 2015 and 2016, a Small Acceptance Vertex Detector (SAVD) was constructed and first measurements of open charm production started in 2016—Figure 6. Vertex resolution has appeared precisely enough (30 μm) to distinguish *D*0 decay. That was possible due to the fixed-target experiment-specific property, where the Lorenz factor *βγ* ≈ 10 makes short-living *D*0 an observable particle, even in such a small acceptance vertex detector.

**Figure 6.** Present NA61/SHINE setup with the SAVD included.

Successful performance of the SAVD in 2016 led to the decision to also use it during the collection of Xe + La data in 2017. About 5 ∗ 106 events of central Xe + La collisions at 150A GeV/c were collected. The Xe + La data are currently under analysis and are expected to lead to physics results in the coming months. One expects to reconstruct several hundreds of *D*0 and *D*¯0 decays. Beyond this, about 4000 *D*0 and *D*¯0 decays can be expected to be reconstructed from the collection of Pb + Pb data in 2018. Further data collection on Pb + Pb collisions and the reconstruction of decays of various open charm mesons are planned by NA61/SHINE for the years 2022–2024. This would be combined with the required detector upgrades, including a full scale, large acceptance vertex detector—now under construction.

Another domain of NA61/SHINE activity will be to measure fragmentation cross-sections relevant for the production of Li, Be, B, C, and N nuclei. These elements are of particular importance for the physics of cosmic rays in the Galaxy. The NA61/SHINE facility has already successfully taken data with light ion beams [34] and can be used with practically no modifications to perform the

needed cross-section measurements at isotope level. The ability to separate different isotopes from fragmentation interactions for a given charge was validated with simulations [35].

**Funding:** The author acknowledges support by the Polish National Science Center under contract No. UMO-2014/15/B/ST2/03752, the COST Actions CA15213 (THOR), CA16117 (ChETEC) and CA16214 (PHAROS) for supporting their networking activities, and the Bogolubov-Infeld Program for supporting the author's stay at JINR Dubna.

**Conflicts of Interest:** The author declare no conflicts of interest.

#### **Abbreviations**

The following abbreviations are used in this manuscript:

#### **References**

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**3. Discussion**

Collagen is an important and diverse biopolymer that has seen a significant increase in applications in food, medicine, cosmetics, and tissue engineering [35] with the highest structural order and the greatest stiffness, is widely used in materials for biomedical applications [36]. Marine collagen has been successfully isolated from marine by-products [1,37,38].There are no reports on the use of lizardfish scales for collagen preparation.

In the present study, we isolated type I collagen from lizardfish scales by using acid and enzymatic extraction methods. It was found that the use of pepsin increased the yield of the collagen extraction, and this could be attributed to the fact that pepsin cleaves the crosslinked molecules in the telopeptide region, leading to further extraction with increased yield. This made the extraction yield of PSC higher than that of ASC. These results agreed with those of Keawdang et al. (2014), who reported that ASC and PSC from yellowfin tuna swim bladders were extracted with yields of 1.07% and 12.10%, respectively [38], and Matmaroh et al. (2011), who reported that ASC and PSC from spotted golden goatfish were extracted with yields of 0.46% and 1.20%, respectively [39]. The difference in the extraction yields could be attributed to the varying cross-linking of collagen fibrils in the different raw materials. In this study, the collagen yields from lizardfish scales were higher than that from bighead carp scales (2.7%) and spotted golden goatfish scales (ASC 0.46% and PSC 1.20%). Both the ASC and PSC had similar UV absorption spectra to those of soft-shelled turtle collagen [23], carp scales collagen [37], and red stingray skin collagen [25]. In addition, we also studied the infrared spectra of the ASC and PSC, and the infrared spectra of the ASC and PSC were similar to the spectra of type I collagen from tilapia skin and scales [18], giant salamander skin [33], and silver carp skin [6], where the Amide I band (1600–1700 cm−1) typically corresponds to the stretching vibration of C=O along the protein polypeptide backbone. This can be used as a positive marker for peptide secondary structure, and therefore it is often used in the analysis [37]. The Amide II band (1500–1600 cm−1) commonly arises from N–H bending coupled with C–N stretching vibrations [40]. The Amide III band (1200–1300 cm−1) arises due to C–N stretching and

N–H in-plane bending from amide linkages, and this is the standard confirming presence of the triple-helical structures of collagen [17]. The absorption peaks of the Amide A band of PSC showed a higher wavenumber than those of the ASC, suggesting that fewer N–H groups in PSC were involved in hydrogen bonding in the polypeptide chain. Similar results were found in chicken feet collagen [41]. It has also been reported in the literature that the hydrolysis of telopeptide by pepsin might increase the free amino group, and this may have led to the higher wavenumber of PSC [40,42]. Moreover, the results of the CD spectrum obtained from the ASC and PSC was similar to the CD spectrum of gulf corvina collagen (positive absorption peaks at 221 nm and negative absorption peaks at 198 nm) [10], *Perinereis nuntia* cuticle collagen (positive absorption peaks at 221 nm and negative absorption peaks at 199 nm) [28], and Nile tilapia skin collagen (positive absorption peaks at 221 nm and negative absorption peaks at 197 nm) [16]. In addition, the XRD spectrum analysis showed that the distance between the molecular chains and the distance between their skeletons of the ASC and PSC were similar to the Pacific cod skin collagen [22] and the cuticle of the *Perinereis nuntia* collagen [28]. The results of the FTIR, CD, and XRD indicated that both the ASC and PSC had a native triple helix conformation, and that the acid and enzymatic extraction methods of collagen had no adverse effects on the molecular integrity of the collagen. The highly porous structure is an important feature of biomedical materials that can influence cell seeding, migration, growth, and other physiological activities [28]. The morphology results suggested that ASC and PSC from lizardfish scales have the potential for biomedical materials [41].

The pyrrolidone ring formed by the amino acids facilitates the strengthening of the triple helix structure of collagen, and this is directly linked to thermal stability and is one feature that determines the potential use of collagen. An analysis of the amino acid content showed that the ASC and PSC had higher amino acid contents than that of the grass carp skin collagen (186 residues/1000) [43], the spotted golden goatfish collagen (ASC 186 residues/1000 and PSC 189 residues/1000, respectively) [39], and the calf skin collagen (221 residues/1000) [44]. Therefore, collagen extracted from the lizardfish scales may have high thermal stability based on the amino acid analysis. Thus, we further characterized the thermal stability of the collagen. In general, collagen obtained from fish species that live in cold environments is often less thermal stable than collagen from fish species that live in warmer environments [39]. The lizardfish (*S. macrops*) is widely distributed in tropical and subtropical waters [45], and the Tmax of lizardfish scale collagen is similar to that of spotted golden goatfish scale collagen (ASC 41.58 ◦C, PSC 41.01 ◦C), a common and abundant species in tropical and sub-tropical regions [39]. In addition, it is higher than cold-water species arabesque greenling skin collagen (ASC 15.7 ◦C and PSC 15.4 ◦C, respectively) [46] and temperate-water fishes grass carp skin collagen (28.4 ◦C) [43]. These results were consistent with the results previously reported, indicating that the collagen obtained from the fish species living in cold environments often had lower hydroxyproline contents exhibited less thermal stability than collagen from fish species living in warmer environments [39]. These results were consistent with the amino acid composition of the above studies, with lizardfish scales collagen containing a higher total amino acid content (ASC 237 residues/1000 residues and 236 residues/1000 residues) than arabesque greenling skin collagen (ASC 159 residues/1000 and PSC 157 residues/1000, respectively) [46] and grass carp skin collagen (186 residues/1000 residues) [43]. Thermal stability is one of the most important properties that determine the potential applications of collagen, and it is related to the total amino acid content, habitat temperature, and body temperature [1]. In addition, the Tmax of lizardfish scale collagen was also higher than calf skin collagen (35.0 ◦C) [44], a collagen from terrestrial sources, and this indicated that collagen from lizardfish scales has the potential for use as an alternative source of terrestrial collagen.

The study of the effect of the NaCl concentration and pH on the relative solubility of collagen can provide useful information for collagen preparation as well as for processing and application. When collagen is used as a source in production in moisturizing cosmetics, solubility is a major determinant. This is because the hydrolyzed substances are used for

cosmetic and medical cream formulations in this industry [47]. The ASC and PSC solutions exhibited the lowest solubility at pH 7 and pH 8, respectively, and this was attributed to the pI of protein with the total net charge of protein molecules being zero when the pH of the solution is equal to the pI [6,48]. In this case, the hydrophobic interaction between collagen molecules is enhanced, leading to aggregation and precipitation of the protein, thereby leading to the low solubility of the solution [21,37]. In contrast, as the solution pH increases above the pI, the net negatively charged residues of the protein increase, causing the ASC and PSC to display a slight increase in solubility at pH levels above 7 and 8, respectively. The differences in the relative solubility of collagen at varying pH levels are related to the molecular properties and conformation of collagen [38]. Kaewdang et al. (2014) [38] reported that the difference in the relative solubility of ASC and PSC at different pHs may be due to the removal of telopeptide regions that affect the protonation or deprotonation of charged amino and carboxyl groups, and this may affect the repulsion of molecules associated with different solubilities. Moreover, the effect of the NaCl concentration on the solubility of collagen solutions showed that the relative solubility of the PSC solutions decreased sharply above a 6% NaCl concentration, while the ASC solutions maintained a high relative solubility (greater than 80%). The relative solubility of the ASC solutions decreased sharply until the NaCl concentration was greater than 10%. The relative solubility of the collagen solutions decreased as the concentration of NaCl increased, and this may have been due to the protein precipitation and salting-out effect [21]. Jongjareonrak et al. (2005) [49] explained that the addition of salt increases the ionic strength and enhances the hydrophobic interaction between protein chains, resulting in a decrease in the solubility of collagen solutions. Thus, the ASC might be less susceptible to the "salting out" effect compared to the PSC [50]. A similar phenomenon has been found in giant croaker swim bladder collagen [48] and silver carp skin [6].

The results of the dynamic frequency scan test revealed that the preparation method markedly affects the rheological parameters, G and G, of ASC and PSC extracted from lizardfish scales. An analysis of the frequency dependence of G and G suggested that the elasticity of the PSC had a greater dependence on frequency than that of the ASC, while the viscosity of the ASC had a greater dependence on frequency than that of the PSC. Moreover, it was noted that the G and G values of PSC were higher than the corresponding G and G" values of ASC between 0.01 and 10 Hz (Figure 6), and these were similar to the collagen from chicken feet. In addition, the G and G of PSC were higher than those of ASC at a scan frequency range of 0.2–10 Hz [41], suggesting that the PSC exhibited good viscoelasticity. It was also observed that G was higher than G for all of the collagen, indicating a greater contribution of viscosity than elasticity in the ASC and PSC from lizardfish scales.

The CCK-8 assay was used to determine the viability of live cells. The relative viability of the HaCaT and MC3T3-E1 cells on the ASC and PSC were greater than 70% during the 48 h of cell culture, indicating that the ASC and PSC from lizardfish scales are not toxic to HaCaT and MC3T3-E1 cells [6]. However, the relative viability of the HaCaT and MC3T3-E1 cells increased during the 48 h of cell culture, suggesting that the lizardfish scales collagen had the ability to promote cell proliferation. And the relative viability of the HaCaT and MC3T3-E1 cells were both higher on ASC than PSC (*p* < 0.05). These results suggested that the ASC was associated with higher cell viability than PSC. Moreover, a morphological examination of the cells showed that both the HaCaT and MC3T3-E1 cells had similar cell growth patterns as the control groups over the culture period (Figure 8). Thus, the results suggested that lizardfish scales ASC and PSC can be used as non-toxic materials in the biomedical field.

### **4. Materials and Methods**