Spectral, statistical and vertex functions in scalar quantum field theory far from equilibrium

TL;DR

This paper investigates the far-from-equilibrium dynamics of relativistic scalar quantum fields, revealing universal scaling behavior, infrared violations of fluctuation-dissipation, and comparing non-perturbative results with kinetic and classical theories.

Contribution

It provides the first detailed analysis of universal scaling functions and exponents for scalar fields far from equilibrium in 3+1 dimensions using a self-consistent expansion.

Findings

Universal scaling exponents and functions identified

Strong infrared violations of fluctuation-dissipation relation observed

Comparison with kinetic and classical theories shows good agreement in certain regimes

Abstract

We compute the far-from-equilibrium dynamics of relativistic scalar quantum fields in 3+1 space-time dimensions starting from over-occupied initial conditions. We determine universal scaling exponents and functions for two-point correlators and the four-vertex in a self-similar regime in time and space or momenta. The scaling form of the momentum-dependent four-vertex exhibits a dramatic fall-off towards low momenta. Comparing spectral functions (commutators) and statistical correlations (anti-commutators) of field operators allows us to detect strong violations of the fluctuation-dissipation relation in this non-perturbative infrared regime. Based on a self-consistent expansion in the number of field components to next-to-leading order, a wide range of interaction strengths is analyzed and compared to weak-coupling estimates in effective kinetic theory and classical-statistical field theory.