Abstract
We argue that non-Abelian gauge fields can be treated as the pseudo-Goldstone vector bosons caused by spontaneous Lorentz invariance violation (SLIV). To this end, the SLIV which evolves in a general Yang–Mills type theory with the nonlinear vector field constraint Tr(AμAμ)=±M2 (M is a proposed SLIV scale) imposed is considered in detail. Specifically, we show that in a theory with an internal symmetry group G having D generators not only the pure Lorentz symmetry SO(1,3), but the larger accidental symmetry SO(D,3D) of the SLIV constraint in itself appears to be spontaneously broken as well. As a result, although the pure Lorentz violation on its own still generates only one genuine Goldstone vector boson, the accompanying pseudo-Goldstone vector bosons related to the SO(D,3D) breaking also come into play properly completing the whole gauge multiplet of the internal symmetry group G taken. Remarkably, they appear to be strictly massless as well, being protected by the starting non-Abelian gauge invariance of the Yang–Mills theory involved. When expressed in terms of the pure Goldstone vector modes, this theory look essentially nonlinear and contains a plethora of Lorentz and CPT violating couplings. However, they do not lead to physical SLIV effects which turn out to be strictly cancelled in all the lowest order processes considered.
Highlights
The old idea[1] that spontaneous Lorentz invariance violation (SLIV) may lead to an alternative theory of quantum electrodynamics still remains extremely attractive in numerous theoretical contexts[2]
The SLIV could generally cause the appearance of massless vector Nambu-Goldstone modes which are identified with photons and other gauge fields underlying the modern particle physics framework like as Standard Model and Grand Unified Theory
While the spontaneous Lorentz violation on its own still generates only one genuine Goldstone vector boson, the accompanying vector pseudo-Goldstone vector bosons (PGB) related to the SO(D, 3D) breaking come into play in the final arrangement of the entire Goldstone vector field multiplet
Summary
The old idea[1] that spontaneous Lorentz invariance violation (SLIV) may lead to an alternative theory of quantum electrodynamics still remains extremely attractive in numerous theoretical contexts[2] (for some later developments, see the papers[3]). There are in general three separate massless Goldstone modes, two of which may mimic the transverse photons polarizations, while the third one must properly be suppressed In this connection, the more instructive laboratory for SLIV consideration proves to be some simple class of the QED type models having from the outset a gauge invariant form, whereas the Lorentz violation is realized through the nonlinear dynamical constraint imposed on the starting vector field Aμ. We mainly address ourselves to the Yang-Mills gauge fields as the possible vector Goldstone modes (Sec.3) once some basic ingredients of the Goldstonic QED model are established in a general SLIV case (Sec.2) This problem has been discussed many times in the literature within quite different contexts, such as the Yang-Mills gauge fields as the Goldstone modes for the spontaneous breaking of general covariance in a higher-dimensional space[17] or for the nonlinear realization of some special infinite parameter gauge group[18].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
