Spontaneous Lorentz Violation in Gauge Theories

TL;DR

This paper investigates spontaneous Lorentz violation in gauge theories by introducing the Sky group, an angle dependent extension of the usual gauge group that captures infrared clouds of soft photons. It constructs a calculable model using a Weyl-like algebra of Sky and intertwiner operators to show how the S-matrix can acquire Lorentz-violating features via a twisted mass term, with parallel abelian and non-Abelian generalizations through Chern-Simons terms. The work highlights the role of asymptotic data in defining superselection sectors, the obstruction to Lorentz invariance in certain Sky sectors, and the nuanced behavior of non-Abelian gauge theories and gravity in this infrared framework.

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.

Figures (1)

• Figure 1: Photons from the distant past arrive at the $t=0$ surface at large distances.