Quantum statistical mechanics of gases in terms of dynamical filling fractions and scattering amplitudes

TL;DR

This paper introduces a finite temperature field theory framework where filling fractions and scattering amplitudes are fundamental, enabling efficient analysis of quantum gases across different dimensions.

Contribution

It develops a novel formalism that decouples zero temperature dynamics from quantum statistical sums using scattering amplitudes as basic variables.

Findings

Derivation of an integral equation akin to the thermodynamic Bethe ansatz.

Application to both relativistic and non-relativistic gases.

Resummation of infinite classes of diagrams through saddle point approximation.

Abstract

We develop a finite temperature field theory formalism in any dimension that has the filling fractions as the basic dynamical variables. The formalism efficiently decouples zero temperature dynamics from the quantum statistical sums. The zero temperature `data' is the scattering amplitudes. A saddle point condition leads to an integral equation which is similar in spirit to the thermodynamic Bethe ansatz for integrable models, and effectively resums infinite classes of diagrams. We present both relativistic and non-relativistic versions.