Note on thermodynamic fermion loop under constant magnetic field

TL;DR

This paper investigates the one-loop effective potential of a thermodynamic fermion loop in a constant magnetic field, analyzing its properties and expansions in different mass regimes.

Contribution

It provides a detailed analysis of the effective potential and its mass expansions, offering insights into fermion behavior under magnetic fields.

Findings

Effective potential interpreted as a sum of energy densities.

Large and small mass expansions derived.

Insights into fermion loop thermodynamics under magnetic fields.

Abstract

The one-loop effective potential of a thermodynamic fermion loop under constant magnetic field is studied. As expected, it can be interpreted literally as a discretized sum of $(D-2)$-dimensional energy density above the Dirac sea. Large/small mass expansions of the potential are also examined.