Spontaneous Lorentz violation: the case of infrared QED

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 [1]. 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. 1

Constrains of Charge-to-Mass Ratios on Noncommutative Phase Space

“…In general there can be a lot of parameters in a quantum field theory with Lorentz violation [57,58]. Here we consider only the following Lagrangian:…”

Infrared effects and the soft photon theorem in massive QED

“…This can also be compared with the formulation of Bagan et al [17]. As pointed out in the Introduction this analysis with exact massless QED is beset with problems like Lorentz symmetry violation [10,18]. The analysis of limit of massive QED to massless is better understood when we use lightcone quantisation.…”

“…Following there are several interesting questions that have been posed in understanding BMS symmetries in gravity [9], effective action in QFT's and gauge theories including non abelian gauge theories. Balachandran et al [10] have pointed out the exact massless photon QED may violate Lorentz symmetry. Similar analysis also leads to color symmetry being broken [11].…”

Novel edge states in self-dual gravity

“…We can generate such elements of G 0 by letting µ(x) approach an angle dependent limit µ ∞ (n), as indicated by (2.11). Then on exponentiation, and restrictingn to a Cauchy slice, we get the Sky group of [10,11] isomorphic to the maps from the celestial sphere S 2 ∞ at infinity to U(1). As µ runs over its possibilities, we get a collection of Sky charges µ ∞ (n) wheren now fixes the representation of G 0 /G ∞ 0 .…”

“…It is important that the redundant degrees of freedom implicit in the Lagrangian do not appear at the level of local observables [2,10,11]. They must by definition commute with G(Λ), but because of the locality, they then commute also with Q(µ).…”