Variational Multi-Time Green's Functions for Nonequilibrium Quantum Fields

TL;DR

This paper develops a variational approach to approximate multi-time Green's functions for nonequilibrium quantum fields, simplifying calculations and enabling analysis of complex systems like curved space quantum field theories.

Contribution

It introduces a variational formalism for multi-time Green's functions that simplifies computations in out-of-equilibrium quantum field theories.

Findings

Provides a tractable method for two-time Green's functions

Applies the formalism to finite temperature ^4 theory in curved space

Demonstrates potential for studying quantum fields in gravitational backgrounds

Abstract

The time-dependent variational principle proposed by Balian and Veneroni is used to provide the best approximation to the generating functional for multi-time Green's functions of a set of (bosonic) observables $Q_{\mu)$. By suitably restricting the trial spaces, the computation of the two-time Green's function, obtained by a second order expansion in the sources, is considerably simplified. This leads to a tractable formalism suited to quantum fields out of equilibrium. We propose an illustration on the finite temperature ${\bf\Phi^4}$ theory in curved space and coupled to gravity.