Quantum Boltzmann equations for mixing scalar fields

TL;DR

This paper develops a systematic derivation of quantum transport equations for scalar fields during electroweak baryogenesis, using the Schwinger-Dyson formalism and gradient expansion, with potential extension to fermions.

Contribution

It presents a formal derivation of quantum Boltzmann equations for scalar fields in a first order phase transition, advancing the theoretical framework for baryon production modeling.

Findings

Derivation of quantum Boltzmann equations from Schwinger-Dyson equations.

Framework applicable to scalar fields, extendable to fermions.

Foundation for more detailed baryogenesis simulations.

Abstract

We report on a work in progress, whose goal is a systematic field theoretical derivation of the quantum transport equations for baryon production in the electroweak plasma at a first order phase transition in the limit of slowly varying background fields (thick wall limit). We start with the Schwinger-Dyson equations for the two point Green function written in the closed time contour (CTC) formalism. The quantum Boltzmann equations for the density matrix arise when the SD-equations are expanded to the first order in the gradients in the on-shell limit. In this paper we consider only scalar fields, but the formalism can easily be extended to fermions.