Star-product Description of Quantization in Second-class Constraint Systems

Nakamura, M.

doi:10.48550/arxiv.1108.4108

Cited by 6 publications

(29 citation statements)

References 16 publications

(25 reference statements)

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“…Following our previous works [2,7,8], we here present the brief review of the constraint star-product quantization formalism of the POM together with the explanation of the notations appearing hereafter.…”

Section: Star-product Quantizationmentioning

confidence: 99%

“…From the commutator algebra C (1) , the constraint-set K (2) obeys the commutator algebra A(K (2) ): [φ (4) i , φ (4) j ] = ihΘ ij , [ψ (2) i , φ (4) j ] = ihδ ij , [ψ (2) i , ψ (2) j ] = 0, (4.14) which shows that K (2) is in the second-class. Therefore, the constraint quantum system S * will be constructed through the star-product quantization formalism of POM [2,4,7].…”

Section: Additional Constraintsmentioning

confidence: 99%

“…which contains the qunatum corrections in the form of the power series of h2n (n ≥ 1) [7], where x ∈ C (2) in O n (x) and O 0 (x) = O(x).…”

Section: I) Accsmentioning

confidence: 99%

“…Through the constraint star-product quantization formalism of POM [2,4,7], we obtain the projected quantum system S (2) in the following way: S (2) = P(2) S (1) = ( P(2) C (1) , P( 2) H (1) , P(2) K (2) ) = (C (2) , H (2) ), (4.32) where P( 2) is the projection operator associated to the ACCS (4.30).…”

Section: I) Accsmentioning

confidence: 99%

“…, the redundant variables [6] associated to the noncommutativities among the resultant canonically conjugate set of the system. Starting with the Lagrangian mentioned above, we shall construct the noncommutative quantum mechanics on the curved space through the constraint star-product quantization formalism of the projection operator method (POM) [7,8]. Imposing the additional constraints to eliminate the redundant degrees of freedom, then, the noncommutative quantum system with the noncommutativity among the coordinates x on the curved space will be constructed exactly and it will be shown in the exact form that the Hamiltonian contains the quantum correction terms due to the noncommutativity associated to the constraint-opetator G(x) and the successive projections of the Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

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Alternative Approach to Noncommutative Quantum Mechanics on a Curved Space

Nakamura¹

2015

Preprint

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Starting with the first-order singular Lagrangian containing the redundant variables, the noncommutative quantum mechanics on a curved space is investigated by the constraint star-product quantization formalism of the projection operator method. Imposing the additional constraints to eliminate the reduntant degrees of freedom, the noncommutative quantum system with noncommutativity among the coordinates on the curved space is exactly constructed. Then, it is shown that the resultant Hamiltonian contains the quantum corrections in the exact form. We further discuss the additional constraints to realize the noncommutativities both of coordinates and momenta on the curved space.

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Section: Star-product Quantizationmentioning

confidence: 99%

Section: Additional Constraintsmentioning

confidence: 99%

“…which contains the qunatum corrections in the form of the power series of h2n (n ≥ 1) [7], where x ∈ C (2) in O n (x) and O 0 (x) = O(x).…”

Section: I) Accsmentioning

confidence: 99%

Section: I) Accsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Alternative Approach to Noncommutative Quantum Mechanics on a Curved Space

Nakamura¹

2015

Preprint

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Lagrangian for the Frenkel electron

Дериглазов

2014

Physics Letters B

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We found Lagrangian action which describes spinning particle on the base of non-Grassmann vector and involves only one auxiliary variable. It provides the right number of physical degrees of freedom and yields generalization of the Frenkel and BMT equations to the case of an arbitrary electromagnetic field. For a particle with anomalous magnetic moment, singularity in the relativistic equations generally occurs at the speed different from the speed of light. Detailed discussion of the ultra-relativistic motion is presented in the work: A. A. Deriglazov and W. G. Ramirez, World-line geometry probed by fast spinning particle, arXiv:1409.4756.Comment: 8 pages, close to published version: paragraph about ultra-relativistic motion is extended, the detailed discussion of this point is presented in arXiv:1409.475

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Canonical Structure of Noncommutative Quantum Mechanics as Constraint System

Nakamura

2014

Preprint

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Starting with the first-order singular Lagrangian, the canonical structure in the noncommutative quantum mechanics with the noncommutativities both of coordinates and momenta is investgated. Using the projection operator method (POM) for the constraint systems and the constraint star-product, the noncommutative quantum system is constructed and the commutator algebra of projected canonically conjugate set(CCS) of the system is derived in the form including all orders of the noncommutativity parameters. We discuss the alternative CCS, which obeys the ordinary noncommutative commutator algebra. The exact CCS is constructed in the framework of the POM, and which is shown to be equivalent to the CCS constructed through the Seiberg-Witten map and the Bopp shift. We further discess the alternative Lagrangian to realize the noncommutativities both of coordinates and momenta.

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Star-product Description of Quantization in Second-class Constraint Systems

Cited by 6 publications

References 16 publications

Alternative Approach to Noncommutative Quantum Mechanics on a Curved Space

Alternative Approach to Noncommutative Quantum Mechanics on a Curved Space

Lagrangian for the Frenkel electron

Canonical Structure of Noncommutative Quantum Mechanics as Constraint System

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