  The generation of a baryon asymmetry via leptogenesis is usually studied by
means of classical kinetic equations whose applicability to processes in the
hot and expanding early universe is questionable. The approximations implied by
the state-of-the-art description can be tested in a first-principle approach
based on nonequilibrium field theory techniques. Here, we apply the
Schwinger-Keldysh/Kadanoff-Baym formalism to a simple toy model of
leptogenesis. We find that, within the toy model, medium effects increase the
vertex contribution to the CP-violating parameter. At high temperatures it is a
few times larger than in vacuum and asymptotically reaches the vacuum value as
the temperature decreases. Contrary to the results obtained earlier in the
framework of thermal field theory, the corrections are only linear in the
particle number densities. An important feature of the Kadanoff-Baym formalism
is that it is free of the double-counting problem, i.e. no need for real
intermediate state subtraction arises. In particular, this means that the
structure of the equations automatically ensures that the asymmetry vanishes in
equilibrium. These results give a first glimpse into a number of new and
interesting effects that can be studied in the framework of nonequilibrium
field theory.
