Continuum Approach to Non-equilibrium Quantum Functional Integral

TL;DR

This paper develops a continuum time approach to derive the non-equilibrium quantum functional integral for non-interacting bosons and fermions, emphasizing boundary conditions and statistical distributions.

Contribution

It introduces a novel continuum time derivation method for non-equilibrium functional integrals, differing from traditional discrete time approaches.

Findings

Derived non-equilibrium functional integral using continuum time.

Accounted for statistical distributions via boundary conditions.

Provided explicit Green's function evaluations.

Abstract

Standard derivations of the functional integral in non-equilibrium quantum field theory are based on the discrete time representation. In this work we derive the non-equilibrium functional integral for non-interacting bosons and fermions using a continuum time approach by accounting for the statistical distribution through the boundary conditions and using them to evaluate the Green's function.