Quantization of dynamical systems subject to second class constraints

Nakamura, Masayoshi; Minowa, H.

doi:10.1063/1.530386

Cited by 6 publications

(9 citation statements)

References 9 publications

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“…To compare the Hamiltonians, we need manifest form of (time-dependent) canonical transformation among the two formulations. Probably, the projection operator method for diagonalization of Dirac brackets [26][27][28] could be used to this aim.…”

Section: Discussionmentioning

confidence: 99%

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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Section: Discussionmentioning

confidence: 99%

Lagrangian for the Frenkel electron

Дериглазов

2014

Physics Letters B

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“…The skew-gradient projection method is found to be useful to formulate classical and quantum constraint dynamics [14,15,37,38,39,40]. In Sect.…”

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confidence: 99%

Weyl’s symbols of Heisenberg operators of canonical coordinates and momenta as quantum characteristics

Krivoruchenko

Faessler

2007

Journal of Mathematical Physics

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The knowledge of quantum phase flow induced under the Weyl's association rule by the evolution of Heisenberg operators of canonical coordinates and momenta allows to find the evolution of symbols of generic Heisenberg operators. The quantum phase flow curves obey the quantum Hamilton's equations and play the role of characteristics. At any fixed level of accuracy of semiclassical expansion, quantum characteristics can be constructed by solving a coupled system of first-order ordinary differential equations for quantum trajectories and generalized Jacobi fields. Classical and quantum constraint systems are discussed. The phase-space analytic geometry based on the star-product operation can hardly be visualized. The statement "quantum trajectory belongs to a constraint submanifold" can be changed e.g. to the opposite by a unitary transformation. Some of relations among quantum objects in phase space are, however, left invariant by unitary transformations and support partly geometric relations of belonging and intersection. Quantum phase flow satisfies the star-composition law and preserves hamiltonian and constraint star-functions.

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“…After finishing this work we got to know about works [44,45,46,47] where projection formalism is discussed.…”

Section: Discussionmentioning

confidence: 99%

Underlying Gauge Symmetries of Second-Class Constraints Systems

Krivoruchenko

Faessler

Râduţâ

et al. 2007

Int. J. Mod. Phys. A

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Gauge-invariant systems in unconstrained configuration and phase spaces, equivalent to secondclass constraints systems upon a gauge-fixing, are discussed. A mathematical pendulum on an n − 1-dimensional sphere S n−1 as an example of a mechanical second-class constraints system and the O(n) non-linear sigma model as an example of a field theory under second-class constraints are discussed in details and quantized using the existence of underlying dilatation gauge symmetry and by solving the constraint equations explicitly. The underlying gauge symmetries involve, in general, velocity dependent gauge transformations and new auxiliary variables in extended configuration space. Systems under second-class holonomic constraints have gauge-invariant counterparts within original configuration and phase spaces. The Dirac's supplementary conditions for wave functions of first-class constraints systems are formulated in terms of the Wigner functions which admit, as we show, a broad set of physically equivalent supplementary conditions. Their concrete form depends on the manner the Wigner functions are extrapolated from the constraint submanifolds into the whole phase space.

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Quantization of dynamical systems subject to second class constraints

Cited by 6 publications

References 9 publications

Lagrangian for the Frenkel electron

Lagrangian for the Frenkel electron

Weyl’s symbols of Heisenberg operators of canonical coordinates and momenta as quantum characteristics

Underlying Gauge Symmetries of Second-Class Constraints Systems

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