  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.
