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The non-commutative electrodynamics based on the canonical Poisson gaugetheory is studied in this paper. For a pure spatial non-commutativity, weinvestigate the plane wave solutions in the presence of a constant and uniformmagnetic background field for the classical electrodynamics in canonicalPoisson gauge theory. We obtain the properties of the medium ruled by thepermittivity and the permeability tensors in terms of the non-commutativeparameter, with the electrodynamics equations in the momentum space. Using theplane wave solutions mentioned, the dispersion relations are modified by themagnetic background, and the correspondent group velocity is affected by thespatial non-commutative parameter. We construct the energy-momentum tensor anddiscuss the conserved components of this tensor in the spatial non-commutativecase. The birefringence phenomenon is showed through the modified dispersionrelations, that depends directly on the non-commutative corrections and also onthe magnetic background field. Using the bound of the polarized vacuum withlaser (PVLAS) experiment for the vacuum magnetic birefringence, we estimate atheoretical value for the spatial non-commutative parameter.

Effects of wave propagation in canonical Poisson gauge theory under an external magnetic field