Gauging the SU(2) Skyrme model

Neto, Jorge Ananias; Neves, C.; Oliveira, W.

doi:10.1103/physrevd.63.085018

Cited by 26 publications

(52 citation statements)

References 40 publications

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“…The mathematics of this formalism is based on the symplectic structure of the phase-space, and therefore, is different from other approaches. Also, in the symplectic formalism there is no distinction between the first and second-class constraints as in the case of the other quantization procedures [37].…”

Section: Symplectic Formalismmentioning

confidence: 99%

“…There are some approaches to perform such a conversion, like BFT method [30][31][32][33][34], the symplectic formalism [25,[35][36][37], and the Noether dualization technique [38][39][40]. As we mentioned before, in order to gauge a system with second-class constraints, we use the symplectic approach in order to embed a non-invariant system in an extended phasespace [41][42][43].…”

Section: Gauge Theories and Constraintsmentioning

confidence: 99%

“…In conclusion, all correction terms G (n) , with n ≥ 3 vanish. Thus, the gauge invariant canonical Hamiltonian, which had been defined as the symplectic potential, is obtained from 37) JHEP01 (2018)017 and the gauged Lagrangian (2.27) will bẽ…”

Section: Jhep01(2018)017mentioning

confidence: 99%

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Lagrange multiplier and Wess-Zumino variable as extra dimensions in the torus universe

Nejad

Dehghani

Monemzadeh

2018

J. High Energ. Phys.

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Abstract:We study the effect of the simplest geometry which is imposed via the topology of the universe by gauging non-relativistic particle model on torus and 3-torus with the help of symplectic formalism of constrained systems. Also, we obtain generators of gauge transformations for gauged models. Extracting corresponding Poisson structure of existed constraints, we show the effect of the shape of the universe on canonical structure of phase-spaces of models and suggest some phenomenology to prove the topology of the universe and probable non-commutative structure of the space. In addition, we show that the number of extra dimensions in the phase-spaces of gauged embedded models are exactly two. Moreover, in classical form, we talk over modification of Newton's second law in order to study the origin of the terms appeared in the gauged theory.

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Section: Symplectic Formalismmentioning

confidence: 99%

Section: Gauge Theories and Constraintsmentioning

confidence: 99%

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Lagrange multiplier and Wess-Zumino variable as extra dimensions in the torus universe

Nejad

Dehghani

Monemzadeh

2018

J. High Energ. Phys.

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“…Most papers about these models are focused on the consistent canonical quantization and their quantum spectrum. This family of models were considered in several approaches including: the symplectic embedding [8,9,10,11], the BFT formalism [9,12,13,17,14,15,16], Stuckelberg field shifting [19,18] or mixed approaches based on first principles of the making gauge systems [9,18,20,21,22].…”

Section: Introductionmentioning

confidence: 99%

First class models from linear and nonlinear second class constraints

et al. 2015

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Two models with linear and nonlinear second class constraints are considered and gauged by embedding in an extended phase space. These models are studied by considering a free non-relativistic particle on the hyper plane and hyper sphere in the configuration space. The gauged theory of the first model is obtained by converting the very second class system to the first class one, directly. In contrast, the first class system related to the free particle on the hyper sphere is derived with the help of the infinite BFT embedding procedure. We propose a practical formula, based on the simplified BFT method, which is practical in gauging linear and some nonlinear second class systems. As a result of gauging these two models, we show that in the conversion of second class constraints to the first class ones, the minimum number of phase space degrees of freedom for both systems is a pair of phase space coordinates. This pair is made up of a coordinate and its conjugate momentum for the first model, but the corresponding Poisson structure of the embedded non-relativistic particle on hyper sphere is a non-trivial one. We derive infinite correction terms for the Hamiltonian of the nonlinear constraints and an interacting gauged Hamiltonian is constructed by summing over them. At

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“…The conversion process starts assuming that two second class constraints must be picked up to construct the gauge symmetry generators, and consequently two additional WZ variables, θ 1 and θ 2 , are introduced. To put our work in perspective with other papers [13,14], we choose the spherical constraint T 2 , Eq. (28) and the constraint T 1 , Eq.…”

Section: General Formalismmentioning

confidence: 99%

Gauging by Symmetries

Neto

Neves

Oliveira

2003

Int. J. Mod. Phys. A

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We propose a new procedure to embed second class systems by introducing Wess-Zumino (WZ) fields in order to unveil hidden symmetries existent in the models. This formalism is based on the direct imposition that the new Hamiltonian must be invariant by gauge-symmetry transformations. An interesting feature in this approach is the possibility to find a representation for the WZ fields in a convenient way, which leads to preserve the gauge symmetry in the original phase space. Consequently, the gauge-invariant Hamiltonian can be written only in terms of the original phase-space variables. In this situation, the WZ variables are only auxiliary tools that permit to reveal the hidden symmetries present in the original second class model. We apply this formalism to important physical models: the reduced-SU(2) Skyrme model, the Chern-Simons-Proca quantum mechanics and the chiral bosons field theory.In all these systems, the gauge-invariant Hamiltonians are derived in a very simple way. *

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Gauging the SU(2) Skyrme model

Cited by 26 publications

References 40 publications

Lagrange multiplier and Wess-Zumino variable as extra dimensions in the torus universe

Lagrange multiplier and Wess-Zumino variable as extra dimensions in the torus universe

First class models from linear and nonlinear second class constraints

Gauging by Symmetries

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