Nonequilibrium Self-Interacting Quantum Fields in Cosmology: The Liouville-Neumann Approach

TL;DR

This paper introduces the Liouville-Neumann approach to nonequilibrium quantum fields, unifying various equations and providing a nonperturbative framework to analyze self-interacting fields in cosmological settings.

Contribution

It presents a unified, nonperturbative Liouville-Neumann approach that extends beyond Gaussian approximation for self-interacting quantum fields in expanding universes.

Findings

Liouville-Neumann approach unifies Schrödinger and LN equations.

At lowest order, matches Gaussian effective potential results.

Proposes a scheme to go beyond Gaussian approximation.

Abstract

We present the so-called Liouville-Neumann (LN) approach to nonequilibrium quantum fields. The LN approach unifies the functional Schr\"{o}dinger equation and the LN equation for time-independent or time-dependent quantum systems and for equilibrium or nonequilibrium quantum systems. The LN approach is nonperturbative in that at the lowest order of coupling constant it gives the same results as those of the Gaussian effective potential at the zero and finite temperature in a Minkowski spacetime. We study a self-interacting quantum field in an expanding Friedmann-Robertson-Walker Universe. By studying a toy model of anharmonic oscillator and finding the underlying algebraic structure we propose a scheme to go beyond the Gaussian approximation.