  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.
