Quantum gauge freedom in the Lorentz violating background. (English) Zbl 1421.81005
The paper deals with a gauge theory under a Lorentz violating framework. In particular, the authors discuss an Abelian \(2\)-form gauge theory invariant under a non-local Lorentz violating gauge theory within the context of Very Special Relativity. To that end, the authors perform the analysis of the \(2\)-form gauge theory by introducing a couple of formalisms, namely the gaugeon fields and the so-called Finite Field-dependent BRST transformation (FFBRST). On the one hand, they consider extra gaugeon fields with the aim to introduce quantum gauge transformations and inspect the implicit quantum gauge freedom. In this case, it is necessary to introduce subsidiary conditions of the Kugo-Ojima and Gupta-Bleuler type in order to define physical quantum states. On the other hand, the authors examine the FFBRST that explicitly introduces field dependent parameters in comparison to the standard BRST transformation. The FFBRST transformation implies a change on the definition of the functional measure through a modified Jacobian that in turn modifies the original effective action by introducing an extra term due to the dependence of the parameters on the fields.
In that sense, one of the main results of the paper is the fact that the FFBRST transformation reproduces the gaugeon modes for the 2-form Abelian gauge field under consideration. The results of the manuscript may be of certain interest from several perspectives that are fundamental to modern approaches to spacetime physics at Planckian scales, in particular to string field theory and loop quantum gravity, where Lorentz symmetry may be broken at this scale.
The article includes a complete list of speculative applications and future work on the lines of Very Special Relativity, AdS/CFT correspondence and within the framework of the Generalized Uncertainty Principles. Even though the manuscript is mostly non-rigorous in both contents and style, the article is complemented with a huge list of references that may serve as a complete guide for the interested reader.
In that sense, one of the main results of the paper is the fact that the FFBRST transformation reproduces the gaugeon modes for the 2-form Abelian gauge field under consideration. The results of the manuscript may be of certain interest from several perspectives that are fundamental to modern approaches to spacetime physics at Planckian scales, in particular to string field theory and loop quantum gravity, where Lorentz symmetry may be broken at this scale.
The article includes a complete list of speculative applications and future work on the lines of Very Special Relativity, AdS/CFT correspondence and within the framework of the Generalized Uncertainty Principles. Even though the manuscript is mostly non-rigorous in both contents and style, the article is complemented with a huge list of references that may serve as a complete guide for the interested reader.
Reviewer: Alberto Molgado (San Luis Potosí)
MSC:
| 81-02 | Research exposition (monographs, survey articles) pertaining to quantum theory |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81T10 | Model quantum field theories |
| 70S15 | Yang-Mills and other gauge theories in mechanics of particles and systems |
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