# Discrete-time construction of nonequilibrium path integrals on the Kostantinov-Perel' time contour

## TL;DR

This paper develops a rigorous method for constructing nonequilibrium path integrals on the Kostantinov-Perel' time contour using a discrete temporal mesh, enabling arbitrary initial states in many-body quantum problems.

## Contribution

It introduces a discrete-time approach to build nonequilibrium path integrals on the Kostantinov-Perel' contour, overcoming limitations of the Schwinger-Keldysh formalism.

## Key findings

- Enables arbitrary initial state preparation in nonequilibrium path integrals.
- Provides a rigorous discrete-time construction method.
- Extends the applicability of path integral techniques to more general initial conditions.

## 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.