Effective Lagrangian at Cubic Order in Electromagnetic Fields and Vacuum Birefringence

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The effective Lagrangian of electromagnetic fields at the cubic order in field strength has been considered. This generalized Lagrangian is motivated by electrodynamics on non-commutative spaces. We find the canonical and symmetrical energy-momentum tensors and show that they possess non-zero traces. The propagation of a linearly polarized laser beam in the external transverse magnetic field is investigated. We evaluate the induced ellipticity which allows us to obtain a constraint on parameters introduced from the PVLAS experimental data.
10 pages, no figures, added note, published version

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