Eur. Phys. J. Plus (2013) 128: 118
https://doi.org/10.1140/epjp/i2013-13118-9

Regular Article

Spontaneous Lorentz violation in gauge theories

¹ Department of Physics, Syracuse University, 13244-1130, Syracuse, N. Y., USA
² Institute of Mathematical Sciences, Chennai, India
³ Instituto Internacional de Fisica, Natal, Brasil
⁴ Centre for High Energy Physics, Indian Institute of Science, 560012, Bangalore, India

^* e-mail: balachandran38@gmail.com

Received: 7 August 2013
Accepted: 7 September 2013
Published online: 18 October 2013

Abstract

Frohlich, Morchio and Strocchi long ago proved that the Lorentz invariance is spontaneously broken in QED because of infrared effects. We develop a simple model where the 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.