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

摘要

In this article it is studied, at variational level, a mathematical setup given bythe Landau-Ginzburg Chern-Simons model for anyons in 2+1-dimensions within the frameworkof dimensional reduced Ue(1) × Ug(1) extended electromagnetism with both vector gauge fields(photons) and pseudo-vector gauge fields (pseudo-photons) such that both magnetic and electricvortexes coexist in the planar system. This model exhibits explicit planar P and T discretesymmetries being the Hall conductivity consistently a tensor and the Dirac quantization on theelectric and magnetic coupling constants is equivalent to the quantization of magnetic flux. It isalso discussed a thickening to 4-dimensions of the model with explicit 4-dimensional P violationwhich allows either for electric and magnetic charge separation, either for the Meissner effect.Although mathematically consistent, the electromagnetic field content for this model does notcoincide with the standard Hall effect being present an extra orthogonal electric and longitudinalmagnetic fields.