Existence Theorem for the Effective Gauge Algebra in the Generalized Canonical Formalism With Abelian Conversion of Second-Class Constraints

Batalin, I. A.; Tyutin, I. V.

doi:10.1142/s0217751x91001581

Cited by 256 publications

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“…We have discussed a systematic method, within the Batalin, Fradkin, Fradkina and Tyutin (BFFT) [2,3] approach, of converting the massive Yang-Mills theory to a gauge invariant theory by extending the phase space. Exploiting an intelligent choice for the symplectic matrix ω ab and the generating matrix X ab , the infinite number of iterative corrections necessary for obtaining the strongly involutive constraints were considerably simplified.…”

Section: Resultsmentioning

confidence: 99%

Hamiltonian embedding of the massive Yang-Mills theory and the generalized Stückelberg formalism

Banerjee

Barcelos-Neto

1997

Nuclear Physics B

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Using the general notions of Batalin, Fradkin, Fradkina and Tyutin to convert second class systems into first class ones, we present a gauge invariant formulation of the massive Yang-Mills theory by embedding it in an extended phase space. The infinite set of correction terms necessary for obtaining the involutive constraints and Hamiltonian is explicitly computed and expressed in a closed form. It is also shown that the extra fields introduced in the correction terms are exactly identified with the auxiliary scalars used in the generalized Stückelberg formalism for converting a gauge noninvariant Lagrangian into a gauge invariant form.

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Section: Resultsmentioning

confidence: 99%

Hamiltonian embedding of the massive Yang-Mills theory and the generalized Stückelberg formalism

Banerjee

Barcelos-Neto

1997

Nuclear Physics B

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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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“…It is important to emphasize that there exists another way, alternative to the procedure of Ref. [13], of handling the secondclass constraints which consists in replacing the second-class constraints by an equivalent set of first-class constraints enlarging the phase space of the system following the BatalinTyutin procedure [14,15]. Once this has been achieved, the problem consists in building the Hamilton-Jacobi theory for systems with first-class constraints, which is well-known [12].…”

Section: Discussionmentioning

confidence: 99%

Hamilton–Jacobi theory for Hamiltonian systems with non-canonical symplectic structures

Martínez-Merino

Montesinos

2006

Annals of Physics

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A proposal for the Hamilton-Jacobi theory in the context of the covariant formulation of Hamiltonian systems is done. The current approach consists in applying Dirac's method to the corresponding action which implies the inclusion of second-class constraints in the formalism which are handled using the procedure of Rothe and Scholtz recently reported. The current method is applied to the nonrelativistic two-dimensional isotropic harmonic oscillator employing the various symplectic structures for this dynamical system recently reported.

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Existence Theorem for the Effective Gauge Algebra in the Generalized Canonical Formalism With Abelian Conversion of Second-Class Constraints

Abstract: The existence of a solution to generating equations for the effective gauge algebra with Abelian conversion of second-class constraints is established. The characteristic arbitrariness of this solution with given initial Hamiltonian and constraints is also studied.

Cited by 256 publications

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Hamiltonian embedding of the massive Yang-Mills theory and the generalized Stückelberg formalism

Hamiltonian embedding of the massive Yang-Mills theory and the generalized Stückelberg formalism

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

Hamilton–Jacobi theory for Hamiltonian systems with non-canonical symplectic structures

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