Scale Invariant Resummed Perturbation at Finite Temperatures

TL;DR

This paper introduces a nonperturbative variational method combined with renormalization group techniques to improve the convergence and scale invariance of thermal field theory calculations, demonstrated on a scalar model.

Contribution

The authors develop a scale-invariant resummed perturbation method that outperforms standard approaches and other resummation techniques in thermal field theories.

Findings

Significantly improved convergence of thermodynamical quantities.

Enhanced scale dependence control compared to traditional methods.

Potential applicability to phase transitions in theories like thermal QCD.

Abstract

We use the scalar model with quartic interaction to illustrate how a nonperturbative variational technique combined with renormalization group (RG) properties efficiently resums perturbative expansions in thermal field theories. The resulting convergence and scale dependence of optimized thermodynamical quantities, here illustrated up to two-loop order, are drastically improved as compared to standard perturbative expansions, as well as to other related methods such as the screened perturbation or (resummed) hard-thermal-loop perturbation, that miss RG invariance as we explain. Being very general and easy to implement, our method is a potential analytical alternative to deal with the phase transitions of field theories such as thermal QCD.