Spontaneous Lorentz Violation in Gauge Theories

TL;DR

This paper demonstrates how Lorentz invariance is spontaneously broken in gauge theories like QED due to infrared effects, by extending the charge group to include direction-dependent transformations, with implications for non-Abelian symmetries and quantum gravity.

Contribution

It introduces a simple model extending the superselected charge group to include Sky transformations, explicitly illustrating Lorentz symmetry breaking in gauge theories.

Findings

Lorentz invariance is spontaneously broken in QED due to infrared effects.

Extension of charge groups to Sky group captures Lorentz symmetry breaking.

Implications for non-Abelian gauge symmetries and quantum gravity are discussed.

Abstract

Frohlich, Morchio and Strocchi long ago proved that Lorentz invariance is spontaneously broken in QED because of infrared effects. We develop a simple model where consequences of this breakdown can be explicitly and easily calculated. For this purpose, the superselected U(1) charge group of QED is extended to a superselected "Sky" group containing direction-dependent gauge transformations at infinity. It is the analog of the Spi group of gravity. As Lorentz transformations do not commute with Sky, they are spontaneously broken. These abelian considerations and model are extended to non-Abelian gauge symmetries. Basic issues regarding the observability of twisted non-Abelian gauge symmetries and of the asymptotic ADM symmetries of quantum gravity are raised.