On the Faddeev–Jackiw symplectic framework for topologically massive gravity

Escalante, Alberto; Rodríguez-Tzompantzi, Omar

doi:10.1140/epjc/s10052-016-4425-x

Cited by 10 publications

(22 citation statements)

References 51 publications

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“…Hence, for s = 1 and the limit γ → ∞, we recover the Dirac canonical structure of Palatini's action [11]. It is important to remark that in the BL model the fields e, A and their canonical momenta have become noncommutative, while in Palatini's action they are commutative.…”

Section: Hamiltonian Dynamics For Three-dimensional Bl Gravitysupporting

confidence: 59%

“…It is important to comment that our results are given in a general form and contain the cases for > 0 and < 0, thus in particular we can reproduce the results given in [17] where the case < 0 was studied. On the other hand, in the limit γ →∝ the action (31) is reduced to S CS (ω) and the Dirac brackets are reduced to those reported in [11], where Palatini's theory was analyzed. Finally, we can observe that in this section we have proved the equivalence between the BL model and the Chern-Simons theory, thus the standard quantization procedure can be performed.…”

Section: Relation With Chern-simons Theorymentioning

confidence: 99%

“…It is important to remark that if some of the Dirac steps is omitted, then it is possible to obtain incomplete results [11,12]. In this manner, an analysis developed on the full phase space and following all the Dirac steps is mandatory.…”

Section: Introductionmentioning

confidence: 99%

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Hamiltonian dynamics and Faddeev–Jackiw formulation of 3D gravity with a Barbero–Immirzi like parameter

Escalante

Manuel-Cabrera

2017

Eur. Phys. J. C

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Section: Hamiltonian Dynamics For Three-dimensional Bl Gravitysupporting

confidence: 59%

Section: Relation With Chern-simons Theorymentioning

confidence: 99%

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Hamiltonian dynamics and Faddeev–Jackiw formulation of 3D gravity with a Barbero–Immirzi like parameter

Escalante

Manuel-Cabrera

2017

Eur. Phys. J. C

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“…There exists, however, a symplectic realization that provides straightforward effective tools for the study of the dynamical structure of Lagrangian field theories, which is geometrically well motivated and is based on the symplectic structure of the space-phase [55][56][57][58][59][60][61], and therefore it is different from Dirac's approach. The advantage of this construction is that we do not need to catalogue the constraints as first-and second-class ones.…”

Section: Jhep01(2021)089mentioning

confidence: 99%

Symplectic realization of two interacting spin-two fields in three dimensions

Rodríguez-Tzompantzi

2021

J. High Energ. Phys.

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We constructed a symplectic realization of the dynamic structure of two interacting spin-two fields in three dimensions. A significant simplification refers to the treatment of constraints: instead of performing a Hamiltonian analysis à la Dirac, we worked out a method that only uses properties of the pre-symplectic two-form matrix and its corresponding zero-modes to investigate the nature of constraints and the gauge structure of the theory. For instance, we demonstrate that the contraction of the zero-modes with the potential gradient, yields explicit expressions for the whole set of constraints on the dynamics of the theory, including the symmetrization condition and an explicit relationship between the coupling and cosmological constants. This way, we further identify the necessary conditions for the existence of a unique non-linear candidate for a partially massless theory, using only the expression for the interaction parameters of the model. In the case of gauge structure, the transformation laws for the entire set of dynamical variables are more straightforwardly derived from the structure of the remaining zero-modes; in this sense, the zero-modes must be viewed as the generators of the corresponding gauge transformations. Thereafter, we use an appropriate gauge-fixing procedure, the time gauge, to compute both the quantization brackets and the functional measure on the path integral associated with our model. Finally, we confirm that three-dimensional bi-gravity has two physical degrees of freedom per space point. With the above, we provide a new perspective for a better understanding of the dynamical structure of theories of interacting spin-two fields, which does not require the constraints to be catalogued as first- and second-class ones as in the case of Dirac’s standard method.

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“…[26] it has been shown that, though technically different, the Faddeev-Jackiw approach and Dirac method are physically equivalent. A recent application of Faddeev-Jackiw (F-J) formalism was discussed in [27], where topologically massive gravity was studied ( other interesting works can be found in references cited here).…”

Section: Introductionmentioning

confidence: 99%

Constrained dynamics of two interacting relativistic particles in the Faddeev-Jackiw symplectic framework

Rodríguez-Tzompantzi

2018

Eur. Phys. J. Plus

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The Faddeev-Jackiw symplectic formalism for constrained systems is applied to analyze the dynamical content of a model describing two massive relativistic particles with interaction, which can also be interpreted as a bigravity model in one dimension. We systematically investigate the nature of the physical constraints, for which we also determine the zero-modes structure of the corresponding symplectic matrix. After identifying the whole set of constraints, we find out the transformation laws for all the set of dynamical variables corresponding to gauge symmetries, encoded in the remaining zero-modes. In addition, we use an appropriate gauge-fixing procedure, the conformal gauge, to compute the quantization brackets (Faddeev-Jackiw brackets) and also obtain the number of physical degree of freedom. Finally, we argue that this symplectic approach can be helpful for assessing physical constraints and understanding the gauge structure of theories of interacting spin-2 fields.PACS numbers:

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On the Faddeev–Jackiw symplectic framework for topologically massive gravity

Cited by 10 publications

References 51 publications

Hamiltonian dynamics and Faddeev–Jackiw formulation of 3D gravity with a Barbero–Immirzi like parameter

Hamiltonian dynamics and Faddeev–Jackiw formulation of 3D gravity with a Barbero–Immirzi like parameter

Symplectic realization of two interacting spin-two fields in three dimensions

Constrained dynamics of two interacting relativistic particles in the Faddeev-Jackiw symplectic framework

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