Very Special Relativity as a background field theory

Abstract

We consider violation of Lorentz invariance in QED induced by a very high frequency background wave. An effective theory is obtained by averaging observables over the rapid field oscillations. This preserves Ward identities and restores translation invariance below the high frequency scale, but only partial Lorentz invariance: we show that the effective theory is C-invariant SIM(2)-QED in Very Special Relativity. Averaging generates the nonlocal terms familiar from SIM(2) theories, while the short-distance behaviour of the background field fermion propagator generates the infinite number of higher-order vertices of SIM(2)-QED.

Version2: References added, discussion extended, results unchanged. To appear in PRD. 8 pages, 3 pdf figures

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• Corrections to the Gyromagnetic Factor in Very Special Relativity
• VSL-Gravity in light of PSR B1913+16 Full Data Set: Upper limits on graviton mass and its theoretical consequences
• Meson spectrum in $QC{D}_2$ revisited