1204.2478 (Zhe Chang et al.)

Lorentz invariance violation and electromagnetic field in an
intrinsically anisotropic spacetime    [PDF]

Zhe Chang, Sai Wang

Recently, Kostelecky [V.A. Kostelecky, Phys. Lett. B {\bf 701}, 137 (2011)] proposed that the spontaneous Lorentz invariance violation (SLIV) for point--like particles is related to Finsler geometry. Finsler spacetime is intrinsically anisotropic and induces naturally the SLIV effects. In this paper, we propose that locally Minkowski spacetime could be a suitable platform to characterize the possible SLIV effects. The electromagnetic field in locally Minkowski spacetime is investigated. The Lagrangian for the electromagnetic field is presented explicitly. It is compatible with the standard model extension (SME), a perturbative SLIV framework. We show the Lorentz--violating Maxwell equations as well as the electromagnetic wave equation. The formal plane wave solution is obtained. To first order, the SLIV effects could be viewed as influence from a slightly anisotropic media on the electromagnetic wave. Depending on concrete characters of the SLIV effects, the lightcone of the anisotropic spacetime is enlarged or narrowed.

View original: http://arxiv.org/abs/1204.2478