$\lambda \phi^{4}$ non equilibrium dynamics and kinetic field theory

TL;DR

This paper investigates non-equilibrium dynamics of the lambda phi^4 model using kinetic field theory, accounting for initial correlations, symmetry breaking, and energy-momentum conservation, with applications to inhomogeneities and Casimir effects.

Contribution

It introduces a reformulation of non-equilibrium lambda phi^4 dynamics via kinetic field theory, including initial correlations and symmetry analysis.

Findings

Broken SO(1,1) symmetry and associated Ward-Takahashi relations.

Generalized kinetic equations for n-point functions.

Identification of Casimir effect in non-equilibrium solutions.

Abstract

Off-shellness and inhomogeneities are in the non-equilibrium dynamics of the lambda phi^4 model are studied using the closed timepath formalism reformulated as kinetic field theory. We take into account initial correlations up to the 4-point functions. The model is shown to exhibit a SO(1,1) symmetry broken by interactions and initial conditions. The divergence of the corresponding Noethercurrent is calculated and the Ward-Takahashi relations for the broken symmetry are given. They constitute a set of generalized integrated kinetic equations for the general n-point functions. We demonstrate that energy-momentum conservation follows from the transport equations. As an application we discuss inhomogeneities and general non-equilibrium conditions in the free field model. In our solution we identify the casimir-effect.