Deriving Boltzmann equations from Kadanoff-Baym equations in curved space-time

In this paper we consider the transition from the Kadanoff-Baym equations to the quantum kinetic equations and then to the Boltzmann equation in curved space-time. As one expects from general considerations, the derived equations appear to be covariant generalizations of the corresponding equations in Minkowski space-time. The formalism will be applied to test approximations commonly made in the computation of the baryon asymmetry in the leptogenesis scenario.

Figure 1

Closed real-time path $\mathcal{C}$.

Figure 2

Two-, three-, and four-loop contributions to the 2PI effective action.

Figure 3

Arrangement of the points along the geodesic.

Figure 4

Feynman diagrams of $2\leftrightarrow 2$ scattering at tree and one-loop levels.