# ar X iv : h ep - t h / 05 11 17 8 v 4 4 J an 2 00 6 Nonlinear QED and Physical Lorentz Invariance

• Published 2009

#### Abstract

The spontaneous breakdown of 4-dimensional Lorentz invariance in the framework of QED with the nonlinear vector potential constraint Aμ = M 2 (where M is a proposed scale of the Lorentz violation) is shown to manifest itself only as some noncovariant gauge choice in the otherwise gauge invariant (and Lorentz invariant) electromagnetic theory. All the contributions to the photon-photon, photon-fermion and fermion-fermion interactions violating the physical Lorentz invariance happen to be exactly cancelled with each other in the manner observed by Nambu a long ago for the simplest tree-order diagrams we extend this fact now to the one-loop approximation (taken in the dimensional regularization scheme) and for both the time-like (M > 0) and space-like (M < 0) Lorentz violation. The way how to reach the physical breaking of the Lorentz invariance in the pure QED case (and beyond) is treated in the flat Minkowskian space-time is also discussed in some detail.

### Cite this paper

@inproceedings{Azatov2009arXI, title={ar X iv : h ep - t h / 05 11 17 8 v 4 4 J an 2 00 6 Nonlinear QED and Physical Lorentz Invariance}, author={Aleksandr Azatov and J . L . Chkareuli}, year={2009} }