Spontaneous Lorentz Violation: The Case of Infrared QED

Understand

It is by now clear that infrared sector of QED has an intriguingly complex structure.

• Based on earlier pioneering works on this subject, two of us recently proposed a simple modification of QED by constructing a generalization of the $U(1)$ charge group of QED to the "Sky" group incorporating the known spontaneous Lorentz violation due to infrared photons, but still compatible in particular with locality.
• There 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 Lorentz symmetry.
• We further elaborate this approach here and investigate in some detail the properties of charged particles dressed by the infrared photons.