3-dimensional Rules for Finite-Temperature Loops

TL;DR

This paper introduces straightforward diagrammatic rules for calculating finite-temperature Euclidean n-point functions using 3-dimensional momentum integrals, eliminating the need for Matsubara sums, and clarifies their physical interpretation.

Contribution

It provides a novel set of rules that simplify finite-temperature calculations by avoiding Matsubara sums, enhancing computational efficiency and conceptual understanding.

Findings

Rules enable direct 3D momentum integral calculations

Elimination of Matsubara sums simplifies finite-temperature computations

Clarifies the physical interaction with the thermal bath

Abstract

We present simple diagrammatic rules to write down Euclidean n-point functions at finite temperature directly in terms of 3-dimensional momentum integrals, without ever performing a single Matsubara sum. The rules can be understood as describing the interaction of the external particles with those of the thermal bath.