Spontaneous Lorentz Violation: The Case of Infrared QED

TL;DR

The paper investigates spontaneous Lorentz violation in infrared QED by promoting the U(1) charge to a Sky group that accounts for the infrared photon cloud surrounding charged particles. It develops a vertex operator formalism to dress charged states with this cloud, derives a Lagrangian term that encapsulates the dressing while preserving locality, and computes the resulting Lorentz-violating effects, including an angle- and momentum-dependent (twisted) fermion mass that alters dispersion relations and spin structure. A detailed analysis shows that boosts are spontaneously broken while rotations may remain intact in certain sectors, and the twisted mass can smear mass and spin in scattering and decays, potentially yielding observable signatures in precision experiments such as muon decay anisotropies. The work also connects these infrared phenomena to non-Abelian superselection and Higgs-related symmetry breaking, suggesting broader implications for symmetry realization in gauge theories and the role of boundary degrees of freedom. Overall, the study provides a concrete framework linking infraredQED structure to measurable Lorentz-violating effects and new forms of mass/spin coupling.

Abstract

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. 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 too.Time dilation formulae for decays should also get corrections. We speculate that these effects could be measured possibly in muon decay experiments.