Discrete-time construction of nonequilibrium path integrals on the Kostantinov–Perel’ time contour

Abstract

Rigorous nonequilibrium actions for the many-body problem are usually derived by means of path integrals combined with a discrete temporal mesh on the Schwinger–Keldysh time contour. The latter suffers from a fundamental limitation: the initial state on this contour cannot be arbitrary, but necessarily needs to be described by a non-interacting density matrix, while interactions are switched on adiabatically. The Kostantinov–Perel’ contour overcomes these and other limitations, allowing generic initial-state preparations. In this article, we apply the technique of the discrete temporal mesh to rigorously build the nonequilibrium path integral on the Kostantinov–Perel’ time contour.