Non-perturbative constraints on perturbation theory at finite temperature

TL;DR

This paper discusses non-perturbative challenges in finite-temperature quantum field theories and how spectral constraints and particle excitations might resolve discrepancies in lattice scalar correlation predictions.

Contribution

It highlights non-perturbative obstructions at finite temperature and proposes spectral constraints and particle excitations as potential solutions.

Findings

Non-perturbative obstructions affect finite-temperature predictions.

Spectral constraints can inform the resolution of these issues.

Particle-like excitations may reconcile theory with lattice results.

Abstract

It has long been understood that the inclusion of temperature in the perturbative treatment of quantum field theories leads to complications that are not present at zero temperature. In these proceedings we report on the non-perturbative obstructions that arise, and how these lead to deviations in the predictions of lattice scalar correlation functions in massive $\phi^{4}$ theory. Using the known non-perturbative spectral constraints satisfied by finite-temperature correlation functions we outline why the presence of distinct particle-like excitations could provide a resolution to these issues.