On the equivalence between bumblebee models and electrodynamics in a non-linear gauge

Abstract

Bumblebee models are effective field theories describing a vector field with a nonzero vacuum expectation value that spontaneously breaks Lorentz invariance. They provide an alternative way of exploring the similarities between theories with spontaneous Lorentz symmetry breaking and gauge theories. The equivalence between bumblebee models with suitable conditions and standard electrodynamics in a non-linear gauge $A_{\mu }{A}^{\mu }-b^2=0$ is taken for granted; however, this point is very subtle and has not yet been fully addressed. The main goal of this paper is to fill in this gap. More precisely, here we study the relation between a bumblebee model, with a smooth potential of the form $V(B_{\mu })=V(B_{\mu }{B}^{\mu }-b^2)$, and standard electrodynamics in the non-linear gauge $A_{\mu }{A}^{\mu }-b^2=0$, both at the classical and quantum levels. Using the Dirac's method we show that after introducing Dirac brackets with suitable initial conditions, the classical dynamics of the bumblebee model corresponds to that of standard electrodynamics in the aforementioned non-linear gauge. In the quantum case we demonstrate that perturbative calculations of Feynman amplitudes to any physical process in each model are indistinguishable. To do this, we show that the Feynman rules and propagators of standard electrodynamics in the non-linear gauge and those describing the bumblebee model are the same.

12 pages

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• Polarization effects in Kerr black hole shadow due to the coupling between photon and bumblebee field
• Some Observable Physical Properties of the Higher Dimensional dS/AdS Black Holes in Einstein-Bumblebee Gravity Theory
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• Charged spherically symmetric and slowly rotating charged black hole solutions in bumblebee gravity
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• Testing Lorentz- and CPT-invariance with ultracold neutrons
• Gravitational Searches for Lorentz Violation with Ultracold Neutrons
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• One-loop radiative corrections in bumblebee-Stueckelberg model
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• Covariant Quantum Gravitational Corrections to Scalar and Tensor Field Models