Quantization of theCP 2 n−1 model

Nakamura, Masayoshi; Minowa, H.; Mishima, Nobuhiko

doi:10.1007/bf02902354

Cited by 3 publications

(3 citation statements)

References 15 publications

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“…We give first description of second-class constraints systems and of the skew-gradient projection formalism. The details are found elsewhere [14,15,37,38,39,40]. If this would not be the case, it could mean that gauge degrees of freedom appear in the system.…”

Section: Characteristics In Classical Constraint Systemsmentioning

confidence: 99%

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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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Section: Characteristics In Classical Constraint Systemsmentioning

confidence: 99%

“…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.…”

mentioning

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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“…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 supersymmetric nonlinear sigma-model

Nakamura

1988

Nuov Cim B

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Quantization of theCP 2 n−1 model

Cited by 3 publications

References 15 publications

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

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

Underlying Gauge Symmetries of Second-Class Constraints Systems

Quantization of supersymmetric nonlinear sigma-model

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