Revealing hidden symmetries and gauge invariance of the massive Carroll-Field-Jackiw model

Abstract

In this paper we have analyzed the improved version of the Gauge Unfixing (GU) formalism of the massive Carroll-Field-Jackiw model, which breaks both the Lorentz and gauge invariances, to disclose hidden symmetries to obtain gauge invariance, the key stone of the Standard Model. In this process, as usual, we have converted this second-class system into a first-class one and we have obtained two gauge invariant models. We have verified that the Poisson brackets involving the gauge invariant variables, obtained through the GU formalism, coincide with the Dirac brackets between the original second-class variables of the phase space. Finally, we have obtained two gauge invariant Lagrangians where one of them represents the Stückelberg form.

Restoring the gauge invariance in non-Abelian second-class theories

“…This expression is the non-Abelian analogue of the expression found in [32,34,35]. Therefore, the expression for the invariant first class function F a , eq.…”

“…The coefficients of this series will be given by successive transformations of the original variabe under the new symmetry generator [30,33]. In quantum field theory, this formalism has been successfully used in Abelian models such as Chern-Simons, Proca and Carroll-Field-Jackiw [30,33,34]. Then, the aim of the present work is to face the issue of the gauge invariance restitution of non-Abelian second-class theories.…”

Improved Gauge-Unfixing Formalism through a Prototypical Second-Class System

“…Note that equation ( 36) is already satisfied and we do not need to modify the constraints T α . In order to calculate H f c in equation (37), as well as other relevant gauge-invariant quantities, instead of using the GU method in its originally conceived form [23,24,25], we employ the much easier equivalent improved GU approach [26] in which we start by obtaining the transformed gauge-invariant tilde variables (q i , pi ). The latter are defined as deformations qi = qi (q k , p k ) ,…”

“…Then this gauge-invariant form can be used to easily obtain the modified Hamiltonian, constraints and all gauge invariant phase space functions. Modern relevant applications of the GU formalism can be seen in references [33,34,35,36,37,38].…”

Massless polarized particle and Faraday rotation of light in the Schwarzschild spacetime

“…The inclusion of an interaction, preserving the physical sector of a free theory with Dirac constraints, generally represents a non trivial task [72][73][74][75][76][77][78][79][80][81][82][83]. Here we discuss the possibility to switch on a non minimal interaction of the massless polarized particle with gravity within the Hamiltonian variational problem (21).…”