Eur. Phys. J. C (2015) 75: 89
https://doi.org/10.1140/epjc/s10052-015-3305-0

Regular Article - Theoretical Physics

Spontaneous Lorentz violation: the case of infrared QED

¹ Physics Department, Syracuse University, Syracuse, NY, 13244-1130, USA
² Department of Physics, Middle East Technical University, 06800, Ankara, Turkey
³ Instituto de Física, Universidade de Brasília, Caixa Postal 04455, Brasília, DF, 70919-970, Brazil
⁴ Departamento de Física Teórica, Facultad de Ciencias, Universidad de Zaragoza, 50009, Zaragoza, Spain
⁵ Centre for High Energy Physics, Indian Institute of Science, Bangalore, 560012, India

^* e-mail: kseckin@metu.edu.tr

Received: 8 January 2015
Accepted: 4 February 2015
Published online: 24 February 2015

Abstract

It is by now clear that the infrared sector of quantum electrodynamics (QED) has an intriguingly complex structure. Based on earlier pioneering work on this subject, two of us recently proposed a simple modification of QED by constructing a generalization of the charge group of QED to the “Sky” group incorporating the well-known spontaneous Lorentz violation due to infrared photons, but still compatible in particular with locality (Balachandran and Vaidya, Eur Phys J Plus 128:118, 2013). It was shown that the “Sky” group is generated by the algebra of angle-dependent charges and a study of its superselection sectors has revealed a manifest description of spontaneous breaking of the Lorentz symmetry. We further elaborate this approach here and investigate in some detail the properties of charged particles dressed by the infrared photons. We find that Lorentz violation due to soft photons may be manifestly codified in an angle-dependent fermion mass, modifying therefore the fermion dispersion relations. The fact that the masses of the charged particles are not Lorentz invariant affects their spin content, and time dilation formulas for decays should also get corrections.