Induced fermionic current at finite temperature

TL;DR

This paper studies how finite temperature, magnetic flux, and chemical potential influence charge and current densities of a massive fermionic field around a cosmic string, revealing periodic and symmetry properties.

Contribution

It provides a detailed analysis of finite temperature expectation values of charge and current densities for fermions with nonzero chemical potential near a cosmic string, including their periodicity and symmetry behaviors.

Findings

Charge density is an even periodic function of magnetic flux.

Azimuthal current is an odd periodic function of magnetic flux.

Results are valid for chemical potential smaller than the fermion mass.

Abstract

Here we analyze the finite temperature expectation values of the charge and current densities for a massive fermionic quantum field with nonzero chemical potential, $\mu$, induced by a magnetic flux running along the axis of an idealized cosmic string. These densities are decomposed into the vacuum expectation values and contributions coming from the particles and antiparticles. Specifically the charge density is an even periodic function of the magnetic flux with the period equal to the quantum flux and an odd function of the chemical potential. The only nonzero component of the current density corresponds to the azimuthal current and it is an odd periodic function of the magnetic flux and an even function of the chemical potential. Both analyzed are developed for the cases where $|\mu |$ is smaller than the mass of the field quanta, $m$.