On the (in)consistency of perturbation theory at finite temperature

TL;DR

This paper investigates the limitations of perturbation theory in finite-temperature scalar quantum field theories, revealing that standard approaches fail at relatively low temperatures due to analytic structure issues, and highlights the importance of non-perturbative effects.

Contribution

The study demonstrates the impact of spectral constraints on finite-temperature correlation functions and emphasizes the need to incorporate non-perturbative thermal effects for consistent perturbative predictions.

Findings

Perturbative predictions worsen at low temperatures without infrared divergences.

Analytic structure of propagators affects perturbation theory accuracy.

Thermoparticle excitations may resolve perturbative inconsistencies.

Abstract

A well-known difficulty of perturbative approaches to quantum field theory at finite temperature is the necessity to address theoretical constraints that are not present in the vacuum theory. In this work, we use lattice simulations of scalar correlation functions in massive $\phi^{4}$ theory to analyse the extent to which these constraints affect the perturbative predictions. We find that the standard perturbative predictions deteriorate even in the absence of infrared divergences at relatively low temperatures, and that this is directly connected to the analytic structure of the propagators used in the expansion. This suggests that the incorporation of non-perturbative thermal effects in the propagators is essential for a consistent perturbative formulation of scalar quantum field theories at finite temperature. By utilising the spectral constraints imposed on finite-temperature correlation functions, we explore how these effects manifest themselves in the lattice data, and discuss why the presence of distinct thermoparticle excitations provides a potential resolution to these issues.