Abstract
We consider the lightlike spontaneous Lorentz invariance violation (SLIV) appearing through the zero “length-fixing” constraint put on a gauge vector field, AμAμ=0, and discuss its physical consequences in the framework of a conventional QED and beyond. Again, as in the timelike and spacelike SLIV cases, AμAμ=±MA2 (MA is a scale of SLIV), while this constraint leads to an emergence of the Nambu-Goldstone modes collected in physical photon, the SLIV itself is still left unobservable unless gauge invariance in the theory is broken. At the same time, a crucial difference with the two former cases is that the asymmetrical vacuum corresponding to the lightlike Lorentz violation appears infinitely degenerated with all other vacua including the symmetrical one. We show that this degeneracy can be lifted out by introducing an extra gauge vector field being sterile with respect to an ordinary matter, though having some potential couplings with the basic Aμ field. A slight mixing of them makes the underlying gauge invariance to be partially broken due to which physical Lorentz invariance occurs broken as well. This may cause a variety of the Lorentz violating processes some of which are briefly discussed.
Highlights
In some analogy with the nonlinear σ-model [1] for pions, one may think a similar ”lengthfixing” constraint put on a gauge vector fieldAμAμ = n2MA2, n2 ≡ nν nν = ±1 (1)could lead to a spontaneous Lorentz invariance violation (SLIV) with a proposed scale MA and a direction determined by an unit vector nν
We considered the lightlike Lorentz violation appearing through the zero ”length-fixing” constraint put on a gauge vector field, AμAμ = 0, and discuss its physical consequences in the framework of a conventional QED and beyond
As in the timelike and spacelike Lorentz violation, AμAμ = ±MA2, while putting this constraint into the Lagrangian leads to an emergence of the zero Nambu-Goldstone modes collected in physical photon, the SLIV itself, is shown to be superficial as it affects only the gauge of the vector field Aμ
Summary
In some analogy with the nonlinear σ-model [1] for pions, one may think a similar ”lengthfixing” constraint put on a gauge vector field. While the constraint (1) leads to an emergence of the zero NG modes collected in physical photon, the SLIV itself, is shown to be superficial as it affects only the gauge of the vector potential Aμ at least in the the approximation mentioned above Later this result was confirmed for the spontaneously broken massive QED [11], non-Abelian theories [12], tensor field gravity [13] and other cases. A crucial difference with the former two cases is that the asymmetrical vacuum corresponding to the lightlike Lorentz violation appears infinitely degenerated with all other vacua including the symmetrical one We show that this degeneracy can be lifted out by introducing an extra gauge vector field being sterile with respect to an ordinary matter, though having some potential couplings with the basic Aμ field.
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