Vortex Solutions in the Chern-Simons Stuekelberg Model

TL;DR

This paper investigates vortex solutions in a (2+1)-dimensional U(1) gauge model with Chern-Simons and Stuekelberg mass terms, revealing how scalar field presence affects flux quantization and Hamiltonian divergence.

Contribution

It introduces vortex solutions in a massive, renormalizable U(1) gauge model with Chern-Simons and Stuekelberg terms, analyzing their properties and divergences.

Findings

Vortex solutions with non-vanishing magnetic flux exist in the model.

Scalar field presence leads to finite, quantized magnetic flux.

Asymptotic behavior depends on the Stuekelberg mass term.

Abstract

Vortex solutions to the classical field equations in a massive, renormalizable U(1) gauge model are considered in (2+1) dimensions. A vector field whose kinetic term consists of a Chern-Simons term plus a Stuekelberg mass term is coupled to a scalar field. If the classical scalar field is set equal to zero, then there are classical configurations of the vector field in which the magnetic flux is non-vanishing and finite. In contrast to the Nielsen-Olesen vortex, the magnetic field vanishes exponentially at large distances and diverges logarithmicly at short distances. This divergence, although not so severe as to cause the flux to diverge, results in the Hamiltonian becoming infinite. If the classical scalar field is no longer equal to zero, then the magnetic flux is not only finite, but quantized and the asymptotic behaviour of the field is altered so that the Hamiltonian no longer suffers from a divergence due to the field configuration at the origin. Furthermore, the asymptotic behaviour at infinity is dependent on the magnitude of the Stuekelberg mass term.