Equivalence between bumblebee models and electrodynamics in a nonlinear gauge

C. A. Escobar and A. Martín-Ruiz
Phys. Rev. D 95, 095006 – Published 11 May 2017

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 nonlinear gauge AμAμ+b2=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(Bμ)=V(BμBμ+b2), and standard electrodynamics in the nonlinear gauge AμAμ+b2=0, both at the classical and quantum levels. Using 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 nonlinear 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 nonlinear gauge and those describing the bumblebee model are the same.

  • Received 12 March 2017

DOI:https://doi.org/10.1103/PhysRevD.95.095006

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Particles & Fields

Authors & Affiliations

C. A. Escobar*

  • CENTRA, Departamento de Física, Universidade do Algarve, 8005-139 Faro, Portugal

A. Martín-Ruiz

  • Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, 04510 México, Distrito Federal, México

  • *cruiz@ualg.pt
  • alberto.martin@nucleares.unam.mx

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Issue

Vol. 95, Iss. 9 — 1 May 2017

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