Faddeev–Jackiw approach of noncommutative space–time electromagnetic theories

Abreu, Éverton M. C.; Fernandes, Rafael L.; Mendes, Albert C. R.; Neto, Jorge Ananias; Paula, Rodrigo M. de

doi:10.1142/s0217751x18501634

Int. J. Mod. Phys. A

2018

DOI: 10.1142/s0217751x18501634

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Faddeev–Jackiw approach of noncommutative space–time electromagnetic theories

Éverton M. C. Abreu

Rafael L. Fernandes

Albert C. R. Mendes

et al.

Abstract: The interest in higher derivatives field theories has its origin mainly in their influence concerning the renormalization properties of physical models and to remove ultraviolet divergences. The noncommutative Podolsky theory is a constrained system that cannot by directly quantized by the canonical way. In this work we have used the Faddeev-Jackiw method in order to obtain the Dirac brackets of the NC Podolsky theory.

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Cited by 4 publications

References 37 publications

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Pauli–Villars regularization elucidated in Bopp–Podolsky’s generalized electrodynamics

Suzuki

Sales

et al. 2019

Eur. Phys. J. C

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We discuss an inherent Pauli-Villars regularization in Bopp-Podolsky's generalized electrodynamics. Introducing gauge-fixing terms for Bopp-Podolsky's generalized electrodynamic action, we realize a unique feature for the corresponding photon propagator with a built-in Pauli-Villars regularization independent of the gauge choice made in Maxwell's usual electromagnetism. According to our realization, the length dimensional parameter a associated with Bopp-Podolsky's higher order derivatives corresponds to the inverse of the Pauli-Villars regularization mass scale Λ, i.e. a = 1/Λ. Solving explicitly the classical static Bopp-Podolsky's equations of motion for a specific charge distribution, we explore the physical meaning of the parameter a in terms of the size of the charge distribution. As an offspring of the generalized photon propagator analysis, we also discuss our findings regarding on the issue of the two-term vs. three-term photon propagator in light-front dynamics. arXiv:1902.07632v1 [hep-th]

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Pauli–Villars regularization elucidated in Bopp–Podolsky’s generalized electrodynamics

Suzuki

Sales

et al. 2019

Eur. Phys. J. C

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Symplectic quantization and general constraint structure of a prototypical second-class system

Gomez,

Pandey,

Thibes

2024

Eur. Phys. J. C

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We discuss a general prototypical constrained Hamiltonian system with a broad application in quantum field theory and similar contexts where dynamics is defined through a functional action obeying a stationarity principle. The prototypical model amounts to a Dirac–Bergmann singular system, whose constraints restrict the actual dynamics to occur within a differential submanifold, as is the case in the major part of field theoretical models with gauge symmetry. We apply the Dirac–Bergmann algorithm in its full generality unraveling a total of 4m second-class constraints and obtain the corresponding Dirac brackets algebra in phase space. We follow with the Faddeev–Jackiw–Barcelos–Wotzasek approach in which the geometric character of the mentioned submanifold is emphasized by means of an internal metric function encoding its symplectic properties. We consider two straightforward examples, applying our general results to constrained motion along a toroidal geometry and to a Lorentz violating toy model in field theory. Since toroidal geometry has been recently used in cosmological models, we suggest how our results could lead to different proposals for the shape of the universe in cosmology.

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On the quantization of FLPR model

Nair,

Gupta

2024

Mod. Phys. Lett. A

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In this paper, we quantize the Friedberg–Lee–Pang–Ren (FLPR) model, using an admissible gauge condition, within the framework of modified Faddeev–Jackiw formalism. Further, we deduce the gauge symmetries and establish off-shell nilpotent and absolutely anti-commuting (anti-)BRST symmetries. We also show that the physical states of the theory are annihilated by the first class constraints which is consistent à la Dirac formalism.

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Faddeev–Jackiw approach of noncommutative space–time electromagnetic theories

Cited by 4 publications

References 37 publications

Pauli–Villars regularization elucidated in Bopp–Podolsky’s generalized electrodynamics

Pauli–Villars regularization elucidated in Bopp–Podolsky’s generalized electrodynamics

Symplectic quantization and general constraint structure of a prototypical second-class system

On the quantization of FLPR model

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