Finite Temperature Quantum Field Theory with Impurities

TL;DR

This paper extends the reflection-transmission algebra framework to finite temperature quantum field theory with impurities in higher dimensions, deriving energy density corrections and analyzing impurity effects.

Contribution

It introduces a novel application of RT algebra to higher-dimensional finite temperature QFT with impurities, including bound state contributions.

Findings

Derived energy density at finite temperature with impurities

Established impurity-induced correction to Stefan-Boltzmann law

Analyzed charge density profiles for various impurities

Abstract

We apply the concept of reflection-transmission (RT) algebra, originally developed in the context of integrable systems in 1+1 space-time dimensions, to the study of finite temperature quantum field theory with impurities in higher dimensions. We consider a scalar field in $(s+1)+1$ space-time dimensions, interacting with impurities localized on $s$-dimensional hyperplanes, but without self-interaction. We discuss first the case $s=0$ and extend afterwards all results to $s>0$. Constructing the Gibbs state over an appropriate RT algebra, we derive the energy density at finite temperature and establish the correction to the Stefan-Boltzmann law generated by the impurity. The contribution of the impurity bound states is taken into account. The charge density profiles for various impurities are also investigated.