Thermal field theory to all orders in gradient expansion

TL;DR

This paper introduces a new perturbative approach to non-equilibrium thermal field theory that avoids singularities and captures complex transient behaviors through time-dependent equations valid to all orders.

Contribution

It develops a novel formulation using non-homogeneous propagators and time-dependent vertices, enabling all-order gradient expansion without quasi-particle approximation.

Findings

Eliminates pinch singularities without resummation.

Derives master equations for distribution functions valid to all orders.

Reveals non-Markovian dynamics dominated by energy-violating processes.

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 all orders in a gradient expansion. For a scalar model, we make a loopwise truncation of these evolution equations, whilst still capturing fast transient behaviour, which is found to be dominated by energy-violating processes, leading to non-Markovian evolution of memory effects.