A prototypical nonlinear second-class system and its BFFT constraints Abelianization

Pandey, Vipul Kumar; Thibes, Ronaldo

doi:10.1142/s0217732322500869

Cited by 10 publications

(12 citation statements)

References 48 publications

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“…Using the relation between newly introduced fields, we will define ω which will give us the possible solution of Equation (34). Here, we will discuss the Abelianiaztion of constraints and Hamiltonian for the Particle motion on the surface V L ð1 ≤ L < NÞ in the Riemann manifold R N (based on [75]).…”

Section: Construction Of the First-class Constraint Theorymentioning

confidence: 99%

“…It is worth to mention here that all the barred quantities defined in Equation ( 49) are function of coordinates x k and fields Θ að2Þ and will take the form of the original unbarred quantities in the limit Θ að2Þ ⟶ 0. Here, any field f ðx k , Θ að2Þ Þ will be written as [75]…”

Section: Construction Of the First-class Constraint Theorymentioning

confidence: 99%

“…The system is shown to contain second-class constraints. The BFFT method will be used to convert the second class constraints to first class one [62][63][64][65][66][67][68][69][70][71][72][73][74][75][76]. Then, the BRST charge and symmetries will be constructed for this BFFT Abelianized system using BFV method [77][78][79] with the help of Faddeev-Senjanovic technique [80,81].…”

Section: Introductionmentioning

confidence: 99%

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Hamiltonian and Lagrangian BRST Quantization in Riemann Manifold II

Pandey

2022

Advances in High Energy Physics

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We have previously developed the BRST quantization on the hypersurface V N − 1 embedded in N -dimensional Euclidean space R N in both Hamiltonian and Lagrangian formulation. We generalize the formalism in the case of L -dimensional manifold V L embedded in R N with 1 ≤ L < N . The result is essentially the same as the previous one. We have also verified the results obtained here using a simple example of particle motion on a torus knot.

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Section: Construction Of the First-class Constraint Theorymentioning

confidence: 99%

Section: Construction Of the First-class Constraint Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Hamiltonian and Lagrangian BRST Quantization in Riemann Manifold II

Pandey

2022

Advances in High Energy Physics

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“…The main claim of the GU formalism then states that those second-class systems can be thought of as coming from an equivalent first-class one fixed in a specific gauge. To set up matters, notation and conventions, let us consider a prototypical second-class system defined by a Lagrangian function of the form [43]…”

Section: A Prototypical Second-class Systemmentioning

confidence: 99%

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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“…This method is known as Batalin-Fradkin-Tyutin (BFT) formalism [13,14]. Since then there has been diverse applications of the BFT formalism [15][16][17][18][19]. On the other hand, Vytheeswaran [6,20,21], based on the idea of Mitra and Rajaraman [22], that does not make use of extra phase-space variables, applied the Lie projection operator directly in the second-class constrained Hamiltonians in order to reveal hidden symmetries.…”

Section: Introductionmentioning

confidence: 99%

Gauge Symmetry of the Chiral Schwinger model from an improved Gauge Unfixing formalism

Ambrosio¹,

Costa²,

F.³

et al. 2023

Preprint

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In this paper, the Hamiltonian structure of the bosonized chiral Schwinger model (BCSM) is analyzed. From the consistency condition of the constraints obtained from the Dirac method, we can observe that this model presents, for certain values of the α parameter, two secondclass constraints, which means that this system does not possess gauge invariance. However, we know that it is possible to disclose gauge symmetries in such a system by converting the original second-class system into a first-class one. This procedure can be done through the gauge unfixing (GU) formalism by acting with a projection operator directly on the original second-class Hamiltonian, without adding any extra degrees of freedom in the phase space. One of the constraints becomes the gauge symmetry generator of the theory and the other one is disregarded. At the end, we have a first-class Hamiltonian satisfying a first-class algebra. Here, our goal is to apply a new scheme of embedding second-class constrained systems based on the GU formalism, named improved GU formalism, in the BCSM. The original second-class variables are directly converted into gauge invariant variables, called GU variables. We have verified that the Poisson brackets involving the GU variables are equal to the Dirac brackets between the original second-class variables. Finally, we have found that our improved GU variables coincide with those obtained from an improved BFT method after a particular choice for the Wess-Zumino terms.

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A prototypical nonlinear second-class system and its BFFT constraints Abelianization

Cited by 10 publications

References 48 publications

Hamiltonian and Lagrangian BRST Quantization in Riemann Manifold II

Hamiltonian and Lagrangian BRST Quantization in Riemann Manifold II

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

Gauge Symmetry of the Chiral Schwinger model from an improved Gauge Unfixing formalism

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