Constrained Gauge Fields from Spontaneous Lorentz Violation

Abstract

Spontaneous Lorentz violation realized through a nonlinear vector field constraint of the type $A_{\mu }{A}^{\mu }=M^2$ ($M$ is the proposed scale for Lorentz violation) is shown to generate massless vector Goldstone bosons, gauging the starting global internal symmetries in arbitrary relativistically invariant theories. The gauge invariance appears in essence as a necessary condition for these bosons not to be superfluously restricted in degrees of freedom, apart from the constraint due to which the true vacuum in a theory is chosen by the Lorentz violation. In the Abelian symmetry case the only possible theory proves to be QED with a massless vector Goldstone boson naturally associated with the photon, while the non-Abelian symmetry case results in a conventional Yang-Mills theory. These theories, both Abelian and non-Abelian, look essentially nonlinear and contain particular Lorentz (and $CPT$) violating couplings when expressed in terms of the pure Goldstone vector modes. However, they do not lead to physical Lorentz violation due to the simultaneously generated gauge invariance.

15 pages, minor corrections, version to be published in Nucl. Phys. B

References in corpus (16)

• Lorentz-Violating Extension of the Standard Model
• Gravity, Lorentz Violation, and the Standard Model
• High-Energy Tests of Lorentz Invariance
• Radiatively Induced Lorentz and CPT Violation in Electrodynamics
• Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity
• Lorentz violation at high energy: concepts, phenomena and astrophysical constraints
• Superluminary Universe: A Possible Solution to the Initial Value Problem in Cosmology
• Primordial Magnetic Fields via Spontaneous Breaking of Lorentz Invariance
• Energy-Momentum Conservation in General Relativity
• Photons and Gravitons as Goldstone Bosons, and the Cosmological Constant
• Spontaneous Breaking of Lorentz Invariance
• Spontaneous Violation of Lorentz Invariance and Ultra-High Energy Cosmic Rays
• Lorentz Invariance and Origin of Symmetries
• Nonlinear QED and Physical Lorentz Invariance
• Spontaneous Lorentz Violation: Non-Abelian Gauge Fields as Pseudo-Goldstone Vector Bosons
• Spontaneously Generated Gauge Invariance

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