Finite Width in out-of-Equilibrium Propagators and Kinetic Theory

TL;DR

This paper derives solutions to out-of-equilibrium propagators in scalar field theory, revealing that equilibrium components have finite width while out-of-equilibrium parts can have zero width, challenging traditional kinetic theory assumptions.

Contribution

It demonstrates that out-of-equilibrium propagators can have zero width, reconciling this with the finite width in equilibrium, and generalizes the fluctuation-dissipation relation.

Findings

Equilibrium propagator has finite width.

Out-of-equilibrium propagator can have zero width.

Effective finite width emerges from gradient expansion.

Abstract

We derive solutions to the Schwinger-Dyson equations on the Closed-Time-Path for a scalar field in the limit where backreaction is neglected. In Wigner space, the two-point Wightman functions have the curious property that the equilibrium component has a finite width, while the out-of equilibrium component has zero width. This feature is confirmed in a numerical simulation for scalar field theory with quartic interactions. When substituting these solutions into the collision term, we observe that an expansion including terms of all orders in gradients leads to an effective finite-width. Besides, we observe no breakdown of perturbation theory, that is sometimes associated with pinch singularities. The effective width is identical with the width of the equilibrium component. Therefore, reconciliation between the zero-width behaviour and the usual notion in kinetic theory, that the out-of-equilibrium contributions have a finite width as well, is achieved. This result may also be viewed as a generalisation of the fluctuation-dissipation relation to out-of-equilibrium systems with negligible backreaction.