Landau-Ginzburg Chern-Simons model with Ue(1)xUg(1) Gauge Symmetry and Internal Pseudo-Photons

TL;DR

This paper explores a Landau-Ginzburg Chern-Simons model with extended U(1) gauge symmetry incorporating pseudo-photons, revealing novel features of vortex coexistence, quantization, and P/T symmetry in planar and 4D systems.

Contribution

It introduces a mathematically consistent extended electromagnetism framework with pseudo-photons, analyzing its implications for anyons, vortex coexistence, and symmetry properties.

Findings

Hall conductivity remains tensorial and quantized.

Electric and magnetic flux quantization conditions are established.

The model predicts additional electric and magnetic field components not seen in standard Hall effect.

Abstract

In this article it is studied, at variational level, a mathematical setup given by the Landau-Ginzburg Chern-Simons model for anyons in 2+1-dimensions within the framework of dimensional reduced Ue(1)xUg(1) extended electromagnetism with both vector gauge fields (photons) and pseudo-vector gauge fields (pseudo-photons) such that both magnetic and electric vortexes coexist in the planar system. This model exhibits explicit planar P and T discrete symmetries being the Hall conductivity consistently a tensor and the Dirac quantization on the electric and magnetic coupling constants is equivalent to the quantization of magnetic flux. It is also discussed a thickening to 4-dimensions of the model with explicit 4-dimensional P violation which allows either for electric and magnetic charge separation, either for the Meissner effect. Although mathematically consistent, the electromagnetic field content for this model does not coincide with the standard Hall effect being present an extra orthogonal electric and longitudinal magnetic fields.