Dirac Quantization of Noncommutative Abelian Proca field

Darabi, F.; Naderi, F.

doi:10.1007/s10773-011-0848-1

Cited by 5 publications

(9 citation statements)

References 12 publications

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“…Using the (hard) Proca constraint structure for N ¼ d obtained before in the master formula (2.2), we count n dof ¼ d − 1 degrees of freedom in the theory. By means of (2.4), it is immediate to certify that this corresponds to two second-class constraints, as explicitly shown, for instance, in [33]. As with the Maxwell field before, we thus find agreement with the Proca field's definition given in [8]: "a real Abelian vector field ½… associated with two second-class constraints."…”

Section: Physical Degrees Of Freedomsupporting

confidence: 78%

Lagrangian constraint analysis of first-order classical field theories with an application to gravity

et al. 2020

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We present a method that is optimized to explicitly obtain all the constraints and thereby count the propagating degrees of freedom in (almost all) manifestly first-order classical field theories. Our proposal uses as its only inputs a Lagrangian density and the identification of the a priori independent field variables it depends on. This coordinate-dependent, purely Lagrangian approach is complementary to and in perfect agreement with the related vast literature. Besides, generally overlooked technical challenges and problems derived from an incomplete analysis are addressed in detail. The theoretical framework is minutely illustrated in the Maxwell, Proca and Palatini theories for all finite d ≥ 2 spacetime dimensions. Our novel analysis of Palatini gravity constitutes a noteworthy set of results on its own. In particular, its computational simplicity is visible, as compared to previous Hamiltonian studies. We argue for the potential value of both the method and the given examples in the context of generalized Proca and their coupling to gravity. The possibilities of the method are not exhausted by this concrete proposal.

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Section: Physical Degrees Of Freedomsupporting

confidence: 78%

Lagrangian constraint analysis of first-order classical field theories with an application to gravity

et al. 2020

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“…The same conclusion also follows from the results obtained in Refs. [65][66][67]. A unified quantization of both the electromagnetic and Proca fields has been performed in Ref.…”

Section: B Fundamentals Of Proca Quantum Mechanicsmentioning

confidence: 99%

Relativistic quantum mechanics of a Proca particle in Riemannian spacetimes

Silenko

2018

Phys. Rev. D

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Relativistic quantum mechanics of a Proca (spin-1) particle in Riemannian spacetimes is constructed. Covariant equations defining electromagnetic interactions of a Proca particle with the anomalous magnetic moment and the electric dipole moment in Riemannian spacetimes are formulated. The relativistic Foldy-Wouthuysen transformation with allowance for terms proportional to the zero power of the Planck constant is performed. The Hamiltonian obtained agrees with the corresponding Foldy-Wouthuysen Hamiltonians derived for scalar and Dirac particles and with their classical counterpart. The unification of relativistic quantum mechanics in the Foldy-Wouthuysen representation is discussed.

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“…(1), (5) and (6), the NC density Lagrangian in (7) can be written in terms of commutative fields aŝ (8) where we can see easily that the standard Proca model is recovered when θ = 0, the commutative field strength tensor is the standard F µν = ∂ µ A ν − ∂ ν A µ . Using the notation in [11], we can define the quantities…”

Section: Noncommutative Proca Modelmentioning

confidence: 99%

“…Since our objective here is to convert second into first-class constraints, it is convenient to study the dynamics of the NC system described above in the scenario of the Hamiltonian framework. In this way, following [11], the next standard step is to calculate the momenta conjugated to A 0 and A i respectively…”

Section: Noncommutative Proca Modelmentioning

confidence: 99%

“…The discussion of the constraints in order to classify them following Dirac's nomenclature, still has little attention in the NC literature. In order to fill this gap we have discussed in this work the constraint analysis and the gauge invariance of the NC version of the Proca model, which was constructed in [11]. In this NC formulation of the Proca model, we will see that it is also a second-class system [11] and in this way, to analyze gauge invariance, we have to convert the system into a first-class one, which is gauge invariant, as well known.…”

Section: Introductionmentioning

confidence: 99%

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Gauge-invariant extensions of the Proca model in a noncommutative space–time

Abreu

Neto

Fernandes

et al. 2016

Int. J. Mod. Phys. A

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The gauge invariance analysis of theories described in noncommutative (NC) space-times can lead us to interesting results since noncommutativity is one of the possible paths to investigate quantum effects in classical theories such as general relativity, for example. This theoretical possibility has motivated us to analyze the gauge invariance of the NC version of the Proca model, which is a second-class system, in Dirac's classification, since its classical formulation (commutative space-time) has its gauge invariance broken thanks to the mass term. To obtain such gauge invariant model, we have used the gauge unfixing method to construct a first-class NC version of the Proca model. We have also questioned if the gauge symmetries of NC theories, are affected necessarily or not by the NC parameter. In this way, we have calculated its respective symmetries in a standard way via Poisson brackets.

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Dirac Quantization of Noncommutative Abelian Proca field

Cited by 5 publications

References 12 publications

Lagrangian constraint analysis of first-order classical field theories with an application to gravity

Lagrangian constraint analysis of first-order classical field theories with an application to gravity

Relativistic quantum mechanics of a Proca particle in Riemannian spacetimes

Gauge-invariant extensions of the Proca model in a noncommutative space–time

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