Vacuum polarization for neutral particles in 2+1 dimensions

TL;DR

This paper explores vacuum polarization effects for neutral particles in 2+1 dimensions, revealing how background electromagnetic fields induce fermion currents and angular momentum, with new examples involving infinite background charge.

Contribution

It introduces a duality framework for neutral particles in 2+1 dimensions and extends known results to cases with infinite background electric charge.

Findings

A uniform background electric current induces a proportional fermion current in the vacuum.

A plane electromagnetic wave does not induce any vacuum current.

Known results for charged particles are adapted to neutral particles with nonuniform background charge.

Abstract

In 2+1 dimensions there exists a duality between a charged Dirac particle coupled minimally to a background vector potential and a neutral one coupled nonminimally to a background electromagnetic field strength. A constant uniform background electric current induces in the vacuum of the neutral particle a fermion current which is proportional to the background one. A background electromagnetic plane wave induces no current in the vacuum. For constant but nonuniform background electric charge, known results for charged particles can be translated to give the induced fermion number. Some new examples with infinite background electric charge are presented. The induced spin and total angular momentum are also discussed.