First-Order Gauge-Invariant Generalization of the Quantum Rigid Rotor

L., de Oliveira, Suzicleide; Santos, Cleberly Evangelista dos; Thibes, Ronaldo

doi:10.1007/s13538-020-00749-8

Cited by 7 publications

(5 citation statements)

References 33 publications

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“…Naturally this brings the possibility of highly unifying the study of such specific models. We mention the non-linear sigma model [55], the quantum rigid rotor [67], generalized quantum rigid rotor [55,68] and the conic constrained particle [69,70] as instances of second-class systems which could be treated along the same lines as the particle on a torus and bumblebee Lorentz symmetry breaking models discussed here. The bumblebee model enjoys a rich physical structure, being able to promote a spontaneous breaking of the Lorentz symmetry, it can be used as a building block for a more ambitious description of our universe [65] -nonetheless its essential constraint structure as a dynamical system can be described by the simple prototypical system (1).…”

Section: Discussionmentioning

confidence: 99%

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BFFT Nonlinear Constraints Abelianization of a Prototypical Second-Class System

Pandey,

Thibes

2021

Preprint

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We apply the BFFT formalism to a prototypical second-class system, aiming to convert its constraints from second-to first-class. The proposed system admits a consistent initial set of second-class constraints and an open potential function providing room for applications to mechanical models as well as field theory such as the non-linear sigma model. The constraints can be arbitralily non-linear, broadly generalizing previously known cases. We obtain a sufficient condition for which a simple closed expression for the Abelian converted constraints and modified involutive Hamiltonian can be achieved. As explicit examples, we discuss a particle on a torus and a spontaneous Lorentz symmetry breaking vector model, obtaining in both situations the full first-class abelianized constraints in closed form and the corresponding involutive Hamiltonian.

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Section: Discussionmentioning

confidence: 99%

“…It can be immediately checked that (71) is in full involution with the constraints (68). However, concerning the last constraint (69) we have…”

Section: Mechanical Example: Particle On a Torusmentioning

confidence: 96%

BFFT Nonlinear Constraints Abelianization of a Prototypical Second-Class System

Pandey,

Thibes

2021

Preprint

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“…The resulting model ( 47) was also briefly discussed in [55] without mention to BRST symmetry. For notational convenience, we write down further 48) in accordance to (29), and note that the general definitions (11) particularize here to…”

Section: Mechanical Example: Elliptical Pathmentioning

confidence: 99%

“…Aiming at a better understanding and generalization of (2) and looking for an alternative general constraints abelianization procedure, we have recently proposed and discussed a few similar models in [6,54,55]. Our current idea to be developed below is to start with a generalized Hamiltonian for a system confined to move along a given geometric hypersurface in a gauge-invariant way.…”

Section: Introductionmentioning

confidence: 99%

“…Our current idea to be developed below is to start with a generalized Hamiltonian for a system confined to move along a given geometric hypersurface in a gauge-invariant way. That Hamiltonian can be thought to come from an equivalent second-class system, as shown in reference [55]. Hence, gauge-invariance is naturally achieved without the need of auxiliary variables in phase space.…”

Section: Introductionmentioning

confidence: 99%

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BRST Analysis and BFV Quantization of the Generalized Quantum Rigid Rotor

Thibes

2020

Preprint

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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.

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General Solution and Canonical Quantization of the Conic Path Constrained Second-Class System

Caires

Thibes

2022

Braz J Phys

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First-Order Gauge-Invariant Generalization of the Quantum Rigid Rotor

Cited by 7 publications

References 33 publications

BFFT Nonlinear Constraints Abelianization of a Prototypical Second-Class System

BFFT Nonlinear Constraints Abelianization of a Prototypical Second-Class System

BRST Analysis and BFV Quantization of the Generalized Quantum Rigid Rotor

General Solution and Canonical Quantization of the Conic Path Constrained Second-Class System

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