Symplectic Quantization of Constrained Systems

Barcelos-Neto, J.; Wotzasek, C.

doi:10.1142/s0217732392001439

Cited by 128 publications

(163 citation statements)

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“…Note that the symplectic formalism [16,17] also gives the same result. (See next section for more details.…”

Section: Improved Dirac Quantization Methodsmentioning

confidence: 75%

“…That this approach is of particular advantage in the case of first-order Lagrangians such as Chern-Simons theories has been emphasized by Faddeev and Jackiw [16]. This symplectic scheme has been applied to a number of models [17,18] and has recently been used to implement the improved DQM embedding program in the context of the symplectic formalism [19,20].…”

Section: Introductionmentioning

confidence: 99%

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Symplectic Embedding and Hamilton–jacobi Analysis of Proca Model

2002

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Following the symplectic approach we show how to embed the Abelian Proca model into a first-class system by extending the configuration space to include an additional pair of scalar fields, and compare it with the improved Dirac scheme. We obtain in this way the desired Wess-Zumino and gauge fixing terms of BRST invariant Lagrangian. Furthermore, the integrability properties of the second-class system described by the Abelian Proca model are investigated using the Hamilton-Jacobi formalism, where we construct the closed Lie algebra by introducing operators associated with the generalized Poisson brackets.

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“…Note that the symplectic formalism [16,17] also gives the same result. (See next section for more details.…”

Section: Improved Dirac Quantization Methodsmentioning

confidence: 75%

Section: Introductionmentioning

confidence: 99%

Symplectic Embedding and Hamilton–jacobi Analysis of Proca Model

2002

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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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“…This approach, the so-called Faddeev-Jackiw (F-J) symplectic formalism (for a detailed account see [37][38][39][40][41][42][43][44]), is useful to obtain in an elegant way several essential elements of a particular physical theory, such as the physical constraints, the local gauge symmetry, 1 In the presence of a cosmological constant, Minkowski space-time is no longer a vacuum solution and the new maximally symmetric solutions are de Sitter (dS) space-time for positive ( dS has SO(3, 1) isometry) and anti-de Sitter (AdS) space-time for negative (AdS has SO(2, 2) isomety). In this respect, the SO(2, 2) group can be seen as a -deformed Poincaré group [56], if → 0 the AdS algebra contracts to the usual Poincaré algebra.…”

Section: Introductionmentioning

confidence: 99%

Gauge symmetry and constraints structure for topologically massive AdS gravity: a symplectic viewpoint

Rodríguez-Tzompantzi

Escalante

2018

Eur. Phys. J. C

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By applying the Faddeev-Jackiw symplectic approach we systematically show that both the local gauge symmetry and the constraint structure of topologically massive gravity with a cosmological constant , elegantly encoded in the zero-modes of the symplectic matrix, can be identified. Thereafter, via a suitable partial gauge-fixing procedure, the time gauge, we calculate the quantization bracket structure (generalized Faddeev-Jackiw brackets) for the dynamic variables and confirm that the number of physical degrees of freedom is one. This approach provides an alternative to explore the dynamical content of massive gravity models.

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Symplectic Quantization of Constrained Systems

Cited by 128 publications

References 0 publications

Symplectic Embedding and Hamilton–jacobi Analysis of Proca Model

Symplectic Embedding and Hamilton–jacobi Analysis of Proca Model

First class models from linear and nonlinear second class constraints

Gauge symmetry and constraints structure for topologically massive AdS gravity: a symplectic viewpoint

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