BRST Analysis and BFV Quantization of the Generalized Quantum Rigid Rotor

Abstract

We identify a strong similarity among several distinct originally second-class systems, including both mechanical and field theory models, which can be naturally described in a gauge-invariant way. The canonical structure of such related systems is encoded into a gauge-invariant generalization of the quantum rigid rotor. We pursue the BRST symmetry analysis and the BFV functional quantization for the mentioned gauge-invariant version of the generalized quantum rigid rotor. We obtain different equivalent effective actions according to specific gauge-fixing choices, showing explicitly their BRST symmetries. We apply and exemplify the ideas discussed to two particular models, namely, motion along an elliptical path and the O(N ) nonlinear sigma model, showing that our results reproduce and connect previously unrelated known gauge-invariant systems.

BFFT Nonlinear Constraints Abelianization of a Prototypical Second-Class System

“…The prototypical system (1) can describe interesting field theory models. We have already mentioned, for instance, the nonlinear sigma model which has been recently studied along similar lines in reference [55]. Here we shall discuss a new application to field theory, namely the Lorentz symmetry breaking bumblebee model [64,65,66].…”

“…In particular, the index sums can be straightforwardly generalized to integrations in field theory models. In reference [55], a Hamiltonian related to a simplified version of (1) has been used to study the BRST symmetries of the nonlinear O(N ) sigma model. In the next section, we briefly review the main idea of the BFFT abelianization procedure and apply it to the prototypical system (1), aiming to convert the 4M constraints ( 4) and ( 9) to (11) to first-class.…”

“…Looking for patterns and searching for uniformity in the BFFT and its modified approaches to a wide range of second-class models in the literature, we propose a prototypical second-class dynamical system which includes many of those models as particular cases. Our prototype system generalizes a previous Hamiltonian model recently published in [55] by allowing a larger set of constraints and including a generic open potential function. The analysis carried out in reference [55] was not directly related to the BFFT formalism.…”

“…Our prototype system generalizes a previous Hamiltonian model recently published in [55] by allowing a larger set of constraints and including a generic open potential function. The analysis carried out in reference [55] was not directly related to the BFFT formalism. Although with a seemingly different approach, the simplified Hamiltonian model of [55] was shown to possess gauge-invariance, being suitable for a consistent functional quantization with BRST symmetry.…”

“…The analysis carried out in reference [55] was not directly related to the BFFT formalism. Although with a seemingly different approach, the simplified Hamiltonian model of [55] was shown to possess gauge-invariance, being suitable for a consistent functional quantization with BRST symmetry. In the present paper, we considerably extend that model in order to properly use the BFFT formalism.…”