Equivalence of Faddeev–Jackiw and Dirac Approaches for Gauge Theories

Garcı́a, J. Antonio; Pons, Josep M.

doi:10.1142/s0217751x97000505

Cited by 54 publications

(61 citation statements)

References 21 publications

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“…Initially the equivalence was discussed in cases when the systems have no constraints [11,12]; but, in a constrained system, the situation was not completely clear, and some argumentation was provided earlier [13,14] as regards the equivalence between the methods. However, recently was presented a proof [15] that the usual Faddeev-Jackiw method and Dirac method were not completely equivalent; namely, one showed that some constraints calculated in the Dirac formalism do not appear in the calculation in the Faddeev-Jackiw formalism.…”

Section: Introductionmentioning

confidence: 99%

Higher-derivative non-Abelian gauge fields via the Faddeev–Jackiw formalism

Bufalo

Pimentel

2014

Eur. Phys. J. C

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In this paper we analyze two higher-derivative theories, the generalized electrodynamics and the AlekseevArbuzov-Baikov effective Lagrangian from the point of view of the Faddeev-Jackiw symplectic approach. It is shown that the full set of constraints is obtained directly from the zeromode eigenvectors, and that they are in accordance with wellknown results from Dirac's theory, a recurrent issue in the literature. The method shows to be rather economical in relation to the Dirac one, obviating thus unnecessary classification and calculations. Afterwards, to conclude we construct the transition amplitude of the non-Abelian theory following a constrained BRST method.

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Section: Introductionmentioning

confidence: 99%

Higher-derivative non-Abelian gauge fields via the Faddeev–Jackiw formalism

Bufalo

Pimentel

2014

Eur. Phys. J. C

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“…are identified as constraints of the theory, and they are not absorbed as it is present in Dirac's method being identified as pseudo-Goldston bosons. Furthermore, we could observe that we arrived to the constraints and the generalized brackets in less steps than Dirac's method, this means that [FJ] is in particular, for the theory under study, more economic than Dirac's procedure [24]. In this manner, we have stablished all the elements for studying the quantization aspects, for example, we can use Dirac's brackets or…”

Section: Conclussions and Prospectsmentioning

confidence: 99%

Dirac and Faddeev–Jackiw quantization of a five-dimensional Stüeckelberg theory with a compact dimension

Escalante

Zárate

2015

Annals of Physics

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A detailed Hamiltonian analysis for a five-dimensional Stüeckelberg theory with a compact dimension is performed. First, we develop a pure Dirac's analysis of the theory, we show that after performing the compactification, the theory is reduced to four-dimensional Stüeckelberg theory plus a tower of Kaluza-Klein modes. We develop a complete analysis of the constraints, we fix the gauge and we show that there are present pseudo-Goldstone bosons. Then we quantize the theory by constructing the Dirac brackets. As complementary work, we perform the Faddeev-Jackiw quantization for the theory under study, and we calculate the generalized Faddeev-Jackiw brackets, we show that both the Faddeev-Jackiw and Dirac's brackets are the same. Finally we discuss some remarks and prospects.

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“…An observation that will be of relevance in what follows is that such canonical transformation in phase space in not canonical with respect to the Dirac bracket (11). This is precisely the trick used to construct a "canonical representation of the constraint surface" [11] where the first class constraints are realized as a subset of momenta and the second class constraints as a proper subset of fields and its associated momenta. In these coordinates the Dirac bracket takes the standard form of an ordinary Poisson structure in Darboux coordinates.…”

Section: Dirac Algorithmmentioning

confidence: 99%

First-Order Actions and Duality

Gaona

Garcı́a

2007

Int. J. Mod. Phys. A

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We consider some aspects of classical S-duality transformations in first order actions taken into account the general covariance of the Dirac algorithm and the transformation properties of the Dirac bracket. By classical S-Duality transformations we mean a field redefinition that interchanges the equations of motion and its associated Bianchi identities. By working from a first order variational principle and performing the corresponding Dirac analysis we find that the standard electro-magnetic duality can be reformulated as a canonical local transformation. The reduction from this phase space to the original phase space variables coincides with the well known result about duality as a canonical non local transformation. We have also applied our ideas to the bosonic string. These Dualities are not canonical transformations for the Dirac bracket and relate actions with different kinetic terms in the reduced space.

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Equivalence of Faddeev–Jackiw and Dirac Approaches for Gauge Theories

Cited by 54 publications

References 21 publications

Higher-derivative non-Abelian gauge fields via the Faddeev–Jackiw formalism

Higher-derivative non-Abelian gauge fields via the Faddeev–Jackiw formalism

Dirac and Faddeev–Jackiw quantization of a five-dimensional Stüeckelberg theory with a compact dimension

First-Order Actions and Duality

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