# On Quantum Fields at High Temperature

## TL;DR

This paper examines the complex perturbative structure of high-temperature quantum fields in QED and QCD plasmas, highlighting challenges in applying thermal perturbation theory at four-loop order due to unique thermal effects.

## Contribution

It reveals a peculiar perturbative structure at high temperature that questions the validity of standard thermal perturbation theory in quantum field calculations.

## Key findings

- Identification of a unique thermal perturbative structure at four-loop order.
- Implications for the reliability of thermal perturbation theory in high-temperature quantum fields.

## Abstract

Revisiting the fast fermion damping rate calculation in a thermalized QED and/or QCD plasma at 4-loop order, focus is put on a peculiar perturbative structure which has no equivalent at zero-temperature. Not surprisingly and in agreement with previous $C^\star$-algebraic analyses, this structure renders the use of thermal perturbation theory quite questionable.