now on we employ units with $\epsilon_0=\hbar=c=1$ and $m$ and $e<0$ denote the electron mass and charge, respectively) [@Landau_b_4_1982; @Fradkin_b_1991; @Dittrich_b_1985]. Importantly, the presence of intense background electromagnetic fields allows for testing QED on a sector where nonlinear effects with respect to the background field strongly affect physical processes and the dynamics of charged particles. This sector is somewhat alternative to the high-energy one successfully investigated via conventional accelerators and it thus can serve as an independent ground test of QED.

High-power optical lasers are becoming a suitable tool to test QED at critical field strengths, which correspond to laser intensities of the order of $10^{29}\;\text{W/cm$^2$}$. In fact, although available lasers have reached peak intensities $I_0$ of the order of $5.5\times 10^{22}\;\text{W/cm$^2$}$ [@Yoon_2019] and upcoming facilities aim at $I_0\sim 10^{23}\text{-}10^{24}\;\text{W/cm$^2$}$ [@APOLLON_10P; @ELI; @CoReLS; @XCELS], the Lorentz invariance of the theory implies that the effective laser field strength at which a process occurs is the one experienced by the charges in their rest frame [@Mitter_1975; @Ritus_1985; @Ehlotzky_2009; @Reiss_2009; @Di_Piazza_2012; @Dunne_2014]. Since the amplitude of the laser field is boosted by a factor of the order of the relativistic Lorentz factor of the charge, an electron for definiteness, one can see that 