  This work covers electron positron pair production in spatially homogeneous
electric (and magnetic) fields. Different field configurations are looked at in
order to study various phenomena including multiphoton pair production,
Sauter-Schwinger pair production and dynamically assisted pair production. The
main focus lies on pulsed, rotating fields with one main frequency component
which are called rotating Sauter pulses. The results are obtained via two
numerical methods, that rest on different theoretical approaches. A generic
method is derived from the Dirac-Heisenberg-Wigner (DHW) formalism which
entails a modified quantum kinetic equation. We call the numerical solution of
this equation the Wigner method. Other types of equations are derived from the
DHW formalism as well and numerically solved with the aim to include magnetic
fields. In the case of rotating Sauter pulses a completely different numerical
method is developed, which is based on a semiclassical approach and therefore
called the semiclassical method. A number of parameter studies are conducted to
understand pair production in rotating Sauter pulses. The Wigner method and the
semiclassical method are compared exhaustively and found to complement each
other. This makes it possible to cover the complete range of parameters of the
rotating Sauter pulse, which helps to calculate the pair production rates for
experiments involving counter-propagating circularly polarized laser light. An
interpretation of the pair production spectra is given. Due to the general
nature of the Wigner method it is possible to study more general field
configurations which include pulses with elliptic polarization, chirp or
bichromatic rotating Sauter pulses. Each of these exhibit interesting features,
including the dynamically assisted Schwinger effect in bichromatic pulses,
which could be useful in planning high-intensity laser experiments.
