Spontaneous pair production from background fields or spacetimes is one of the most prominent phenomena predicted by quantum field theory. The Schwinger mechanism of production of charged pairs by a strong electric field and the Hawking radiation of
all species of particles from a black hole are the consequence of nonperturbative quantum effects. In this review article, the vacuum structure and pair production is reviewed in the in-out formalism, which provides a consistent framework for quantum field theory in the sense that the complex action explains not only the vacuum persistence but also pair production. The current technology of intense lasers is still lower by a few order than the Schwinger limit for electron-positron pair production, while magnetic fields of magnetars on the surface are higher than the Schwinger limit and even higher at the core. On the other hand, the zero effective mass of electron and hole in graphene and Dirac or Weyl semimetals will open a window for experimental test of quantum electrodynamics (QED) phenomena in strong fields.
Some astrophysical objects are supposed to have very strong electromagnetic fields above the critical strength. Quantum fluctuations due to strong electromagnetic fields modify the Maxwell theory and particularly electric fields make the vacuum unsta
ble against pair production of charged particles. We study the strong field effect such as the effective action and the Schwinger pair production in scalar QED.
The divergent part of the one-loop Vilkovisky unique effective action for quantum Einstein gravity is evaluated in the general parametrization of the quantum field, including the separated conformal factor. The output of this calculation explicitly d
emonstrates the parametrization and conformal gauge independence of the unique effective action with the configuration space metric chosen following Vilkoviskys prescription.
The mean-square width of the energy profile of bosonic string is calculated considering two boundary terms in the effective action. The perturbative expansion of the Lorentz-invariant boundary terms at the second and the fourth order in the effective
action is taken around the free Nambu-Goto action. The calculation are presented for open strings with Dirichlet boundary condition on cylinder.
We use the evolution operator method to find the one-loop effective action of scalar and spinor QED in electric field backgrounds in terms of the Bogoliubov coefficient between the ingoing and the outgoing vacua. We obtain the exact one-loop effectiv
e action for a Sauter-type electric field, E_0 sech^2 (t/tau), and show that the imaginary part correctly yields the vacuum persistence. The renormalized effective action shows the general relation between the vacuum persistence and the total mean number of created pairs for the constant and the Sauter-type electric field.