show up when trying to generalize the concept of local thermal equilibrium in quantum field theory in curved spacetime. Furthermore, the ambiguities and anomalies of the stress energy tensor do play a role in semiclassical gravity (and semiclassical cosmology), and we will come back to this point a bit later.

Local Thermal Equilibrium
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LTE States on Minkowski Spacetime
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Following the idea of Buchholz, Ojima and Roos [@BOR], local thermal equilibrium (LTE, for short) states are states of a quantum field for which local, intensive thermal quantities, such as — most prominently — temperature and pressure can be defined, and take the values they would assume for a thermal equlibribum state. Here, “local” means, in fact, at a collection of spacetime points. We will soon be more specific about this.

Although the approach of [@BOR] covers also interacting fields, for the purposes of this contribution we will restrict attention to the quantized linear scalar field; furthermore, we start by introducing the concept of LTE states on Minkowski spacetime. Consider the quantized massive linear field $\Phi_0$ on Minkowski spacetime, in its usual vacuum representation, subject to the field equation $(\Box + m^2)\Phi_0 = 0$ (to be understood in the sense 