Mathematical Feature of Gauge Theory

Ebrahimi, Aghileh S.; Monemzadeh, M.

doi:10.1007/s10773-014-2163-0

Cited by 5 publications

(11 citation statements)

References 14 publications

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“…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%

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: Gauge Theories and Constraintsmentioning

confidence: 99%

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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“…So, the gauged model of anyons remains anyonic. But, in this manner, we propose another procedure, like BFT [26,27,28,29,30] with which we are working now, within which we predict that the mentioned constraint will be affect. Hence, after gauging the anyon's Hamiltonian, we derive an interacting model.…”

Section: Discussionmentioning

confidence: 99%

Fundamental Symmetries of the Modified Anyonic Particle

Nejad,

Dehghani,

Monemzadeh

2015

Preprint

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We try to increase the fundamental symmetries of the anyonic particle with the help of the symplectic formalism of constrained systems and gauging the model. The main idea of this approach is based on the embedding of the model in an extended phase space. After the gauging process had done, we obtain generators of gauge transformations of the model. Finally, by extracting the corresponding Poisson structure of all constraints, we compare the effect of gauging on the the phase spaces, the number of physical degrees of freedom, and canonical structures of both primary and gauged models.

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“…In conformity with the well-established GU formalism, in this section we construct a new gauge-invariant parent model, related to the second-class system characterized by equations ( 26) to (31), in which only half from the 2M true constraints (6) shall be identified as actually originally first-class -the remaining half representing possible subsidiary gaugefixing conditions. As discussed in the last section, the M statements T α (q k ) = 0 can be naturally regarded as the main holonomic conditions under which the system dynamically evolves.…”

Section: Improved Gauge-unfixing Formalismmentioning

confidence: 99%

“…within the framework of the sought-for gauge-invariant parent system. For this assertion to be completely true, we have to replace the original second-class Hamiltonian function (26) by a suitable equivalent first-class one H f c and, accordingly, modify the set of relations (29) to (31) to…”

Section: Improved Gauge-unfixing Formalismmentioning

confidence: 99%

“…A projection operator acting on phase space is introduced in references [24,25] to tackle the modified Hamiltonian and other gauge invariant functions, with a corresponding direct application to the chiral Schwinger model in [29]. Interesting comparisons between the GU and BFFT formalisms can be seen in [30,31]. Certainly one of the main drawbacks of the BFFT conversional approach is the introduction of too many auxiliary variables, one for each first-class-to-be constraint.…”

Section: Introductionmentioning

confidence: 99%

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

Neto¹,

Morais²,

Thibes³

2022

Preprint

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We contextualize the improved gauge-unfixing (GU) formalism within a rather general prototypical second-class system, obtaining a corresponding first-class equivalent description enjoying gauge invariance which can be applied to several situations. The prototypical system is chosen to represent a considerable class of relevant models in field theory. By considering the improved version of the GU formalism, we show that any gauge-invariant function can be obtained in terms of a specific deformation in phase space, benefiting thus from the fact that no auxiliary variables are needed in the process. In this way, the resulting converted first-class system is constructed out of the same original canonical variables, preserving the number of degrees of freedom. We illustrate the technique with an application to the nonlinear sigma model.

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Mathematical Feature of Gauge Theory

Cited by 5 publications

References 14 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

Fundamental Symmetries of the Modified Anyonic Particle

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

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