Very Special Relativity as a background field theory

TL;DR

This paper derives an effective theory from high-frequency background waves in QED, revealing a partial Lorentz invariance consistent with Very Special Relativity, and introduces nonlocal terms and higher-order vertices.

Contribution

It demonstrates how averaging over rapid oscillations in a high-frequency background leads to an effective SIM(2)-invariant QED with nonlocal terms and higher-order interactions.

Findings

Effective theory preserves Ward identities and translation invariance.

The resulting theory exhibits SIM(2) invariance and C-invariance.

Nonlocal terms and higher-order vertices are generated from the background field.

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.