# Casimir effect and Stefan-Boltzmann law in Yang-Mills theory at finite temperature

## TL;DR

This paper investigates the Casimir effect and Stefan-Boltzmann law within finite-temperature Yang-Mills theory using Thermo Field Dynamics, focusing on gluon self-interactions and their implications for non-Abelian gauge theories.

## Contribution

It introduces a finite-temperature analysis of Yang-Mills theory applying Thermo Field Dynamics to compute Casimir and Stefan-Boltzmann effects, including gluon self-interactions.

## Key findings

- Calculated the Stefan-Boltzmann law for gluons at finite temperature.
- Derived the Casimir effect in non-Abelian gauge theory at finite temperature.
- Included analysis of massless quark responses in the gauge theory.

## Abstract

A non-Abelian gauge theory describes the strong interactions among particles with the commutator of generators are non-zero. An $SU(3)$ gauge theory describes the interactions that lead to nuclear forces among particles. The Lagrangian density refers to fermions with colour and flavour and the gauge field quanta implying gluons. The gauge theory is treated at finite temperature using the Thermo Field Dynamics (TFD). Using self interaction of gluons the Stefan-Boltzmann law and the Casimir effect are calculated at finite temperature. An appendix is attached to give a response of a massless quarks in gauge theory.