Equivalence between bumblebee models and electrodynamics in a nonlinear 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 AµA µ −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 (Bµ) = V (BµB µ − b 2 ), and standard electrodynamics in the non-linear gauge AµA µ − 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.

GUP modified Hawking radiation in bumblebee gravity

“…(40) into Eqs. (38) and (39), we find out the identical equations for X and Y equations. Thus, we have…”

“…For other studies demonstrating the physical effects (quasinormal modes, thermodynamics, etc.) of the bumblebee field, the reader may refer to [33][34][35][36][37][38][39][40][41][42] and references therein.…”

On the quantum equivalence of an antisymmetric tensor field with spontaneous Lorentz violation

“…This may serve as a motivation for future studies on quantum equivalence. An interesting problem is that of Bumblebee model, whose equivalence has although been checked in specific contexts [37], an effective action analysis has not yet been performed. It must also be pointed out that calculating heat kernel for the present problem would be useful while studying gravitational corrections in cosmological contexts.…”

Polarization effects in Kerr black hole shadow due to the coupling between photon and bumblebee field

“…is supposed to own a minimum at B µ B µ = ∓b 2 . The condition B µ B µ = ∓b 2 is satisfied when the vector field has a nonzero vacuum value [14][15][16][17][18][19][20][21][22][23][24]…”

“…value of a bumblebee field B µ under a suitable potential. Recently, the bumblebee gravity model has been extensively studied in literature [16][17][18][19][20][21][22][23][24]. An exact Schwarzschild-like black hole solution in this bumblebee gravity model is obtained and some classical tests are studied [14].…”