The Pressure of Hot $g^2 \phi^4$ Theory at order $g^5$

TL;DR

This paper calculates the $g^5$ order contribution to the pressure of massless $g^2 \, \phi^4$ theory at finite temperature, clarifying previous issues and optimizing the calculation method.

Contribution

It provides the explicit $g^5$ order pressure contribution and clarifies the optimal rearranged Lagrangian for such thermal field theory calculations.

Findings

Explicit $g^5$ order pressure contribution obtained.

Reconsideration of lower order contributions.

Clarification of optimal Lagrangian choice.

Abstract

The order $g^5$ contribution to the pressure of massless $g^2 \phi^4$ theory at nonzero temperature is obtained explicitly. Lower order contributions are reconsidered and two issues leading to the optimal choice of rearranged Lagrangian for such calculations are clarified.