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In this article it is studied, at variational level, a mathematical setupgiven by the Landau-Ginzburg Chern-Simons model for anyons in 2+1-dimensionswithin the framework of dimensional reduced Ue(1)xUg(1) extendedelectromagnetism with both vector gauge fields (photons) and pseudo-vectorgauge fields (pseudo-photons) such that both magnetic and electric vortexescoexist in the planar system. This model exhibits explicit planar P and Tdiscrete symmetries being the Hall conductivity consistently a tensor and theDirac quantization on the electric and magnetic coupling constants isequivalent to the quantization of magnetic flux. It is also discussed athickening to 4-dimensions of the model with explicit 4-dimensional P violationwhich allows either for electric and magnetic charge separation, either for theMeissner effect. Although mathematically consistent, the electromagnetic fieldcontent for this model does not coincide with the standard Hall effect beingpresent an extra orthogonal electric and longitudinal magnetic fields.

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