  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.
