Free Fermions at Finite Temperature: An Application of the Non-Commutative Algebra

TL;DR

This paper introduces a novel algebraic method leveraging Grassmann variables to compute high-temperature expansions of fermionic models, simplifying calculations by avoiding path integrals, and applies it to free Dirac fermions.

Contribution

The paper presents a new algebraic approach using Grassmann generators for calculating fermionic partition functions at high temperatures, applicable in any dimension.

Findings

Successfully applied to free Dirac fermions

Recovers known results in the literature

Simplifies calculations by avoiding path integrals

Abstract

Charret et. al. applied the properties of the Grassmann generators to develop a new method to calculate the coefficients of the high temperature expansion of the grand canonical partition function of self-interacting fermionic models in any d-dimensions (d>=1). The method explores the anti-commuting nature of fermionic fields and avoids the calculation of the fermionic path integral. We apply this new method to the relativistic free Dirac fermions and recover the known results in the literature.