In these lecture notes we give an introduction to the kinetic equation
approach to pair production form the vacuum in strong, time-dependent external
fields (dynamical Schwinger process). We first give a derivation of the kinetic
equation with the source term for the case of fermions starting from the Dirac
equation and for bosons from the Klein-Gordon equation. In a second part we
discuss the application of the approach to the situation of external field
pulses as single-sheeted functions of time (like the Sauter-pulse) and as
multi- sheeted functions approximating the situation in the focal point of
counter-propagating laser beams. Special emphasis is on the discussion of the
time evolution of the system that exhibits the characteristics of a
field-induced phase transition for which we discuss the behaviour of the
entropy and particle density of the system. We give an outlook to applications
of the approach in describing particle production in strong fields formed in
particle and nuclear collisions.Comment: 23 pages, 7 figures, Lecture Notes based on arXiv:hep-ph/9809227 and
arxiv:1607.08775; to appear in Proceedings of the Helmholtz International
Summer School on "Quantum Field Theory at the Limits: From Strong Fields to
Heavy Quarks", July 18-30, 2016, Dubna, Russi
