Perturbative Non-Equilibrium Thermal Field Theory to all Orders in Gradient Expansion

TL;DR

This paper introduces a novel perturbative approach to non-equilibrium thermal field theory that avoids pinch singularities and captures complex transient dynamics through all-order gradient expansions.

Contribution

It develops a new perturbative framework using non-homogeneous propagators and time-dependent vertices, enabling all-order gradient expansion and non-Markovian evolution analysis.

Findings

Eliminates pinch singularities without quasi-particle approximation

Derives master equations valid to all orders in perturbation and gradient expansion

Reveals energy-violating processes dominate transient dynamics

Abstract

We present a new perturbative formulation of non-equilibrium thermal field theory, based upon non-homogeneous free propagators and time-dependent vertices. The resulting time-dependent diagrammatic perturbation series are free of pinch singularities without the need for quasi-particle approximation or effective resummation of finite widths. After arriving at a physically meaningful definition of particle number densities, we derive master time evolution equations for statistical distribution functions, which are valid to all orders in perturbation theory and to all orders in a gradient expansion. For a scalar model, we perform a perturbative loopwise truncation of these evolution equations, whilst still capturing fast transient behaviour, which is found to be dominated by energy-violating processes, leading to the non-Markovian evolution of memory effects.