Abstract
Even though models with spontaneous Lorentz-symmetry breaking also damage gauge invariance, an interesting possibility that emerges is to interpret the resultant massless Goldstone bosons as the gauge bosons of the related gauge theory. In this contribution we review the conditions under which gauge invariance is recovered from such models. To illustrate our general approach we consider the classical Abelian bumblebee and Nambu models. In the former case we prove its connection with electrodynamics by a procedure which takes proper care of the gauge-fixing conditions. In the case of the Abelian Nambu model its relation with electrodynamics is established in such a way that the generalization to the non-Abelian case is straightforward.
Highlights
An alternative way of looking at global active Lorentz-symmetry breaking (LSB) is to consider its spontaneous version, which yields Goldstone bosons (GBs) of tensorial character as opposed to the standard Higgs mechanism with scalar content
Even though models with spontaneous Lorentz-symmetry breaking damage gauge invariance, an interesting possibility that emerges is to interpret the resultant massless Goldstone bosons as the gauge bosons of the related gauge theory. In this contribution we review the conditions under which gauge invariance is recovered from such models
To illustrate our general approach we consider the classical Abelian bumblebee and Nambu models. In the former case we prove its connection with electrodynamics by a procedure which takes proper care of the gauge-fixing conditions
Summary
An alternative way of looking at global active Lorentz-symmetry breaking (LSB) is to consider its spontaneous version, which yields Goldstone bosons (GBs) of tensorial character as opposed to the standard Higgs mechanism with scalar content. We have provided a proof of the quantum equivalence of the ANM and ED in the gauge BμBμ − n2b2 = 0, to all orders in perturbation theory, under the previously stated requirements In this case the ANM is coupled to the conserved fermionic current eΨγμΨ and the Gauss law is imposed upon the zeroth-order Lagrangian which reduces to ED in the axial gauge for t → ∞ [17]. The study of Nambu models poses the following general problem in gauge theories: how do we recover gauge invariance after breaking it by the imposition of an additional constraint among the coordinates? We dealt with this problem in Ref. [14] by introducing what we call an extended Nambu model, defined by a Lagrangian density yielding first-class constraints only, plus an arbitrary relation among the coordinates restricted alone by very general conditions
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