Green's functions in the presence of a bubble wall

TL;DR

This paper develops field theoretical tools to analyze quantum phenomena like transition radiation during Higgs bubble expansion in the early universe, focusing on propagators with varying particle masses across the bubble wall.

Contribution

It introduces a novel method for constructing propagators and quantization in the presence of a bubble wall using eigenfunction expansion and spectral functions.

Findings

Integral representations of Bosonic and Fermionic propagators with varying masses

A new approach to field quantization near bubble walls

Application to early universe phase transition phenomena

Abstract

Field theoretical tools are developed so that one can analyze quantum phenomena such as transition radiation that must have occurred during the Higgs condensate bubble expansion through plasma in the early universe. Integral representations of Bosonic and Fermionic propagators are presented for the case that particle masses are varied continuously during the passage through the bubble wall interface between symmetry-restored and symmetry-broken regions. The construction of propagators is based on the so-called eigenfunction expansion method associated with self-adjoint differential operators, developed by Weyl, Stone, Titchmarsh, Kodaira and several others. A novel method of field quantization in the presence of the bubble wall is proposed by using the spectral functions introduced in constructing the two-point Green's functions.