Fermion Condensate and Vacuum Current Density Induced by Homogeneous and Inhomogeneous Magnetic Fields in (2+1)-Dimensions

TL;DR

This paper investigates how external magnetic fields induce fermion condensates and vacuum currents in (2+1)-dimensional space, using both perturbative and non-perturbative methods, revealing proportionality to the magnetic field in large flux limits.

Contribution

It provides a non-perturbative calculation of the fermion propagator in a uniform magnetic field using the Schwinger-Dyson equation, extending understanding of magnetic field effects in lower-dimensional quantum field theories.

Findings

Both perturbative and non-perturbative quantities are proportional to the magnetic field in large flux limit.

The fermion propagator was obtained non-perturbatively for a uniform magnetic field.

Induced condensate and current density scale linearly with magnetic flux in the studied regimes.

Abstract

We calculate the condensate and the vacuum current density induced by external static magnetic fields in (2+1)-dimensions. At the perturbative level, we consider an exponentially decaying magnetic field along one cartesian coordinate. Non-perturbatively, we obtain the fermion propagator in the presence of a uniform magnetic field by solving the Schwinger-Dyson equation in the rainbow-ladder approximation. In the large flux limit, we observe that both these quantities, either perturbative (inhomogeneous) and non-perturbative (homogeneous), are proportional to the external field, in agreement with early expectations.