Can Dirac quantization of constrained systems be fulfilled within the intrinsic geometry?

Xun, D. M.; Liu, Q.H.

doi:10.1016/j.aop.2013.11.017

Cited by 33 publications

(30 citation statements)

References 21 publications

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“…with base S 2 , standard fiber F 2 , projection map , and structure group given by the transformations (112) and (113). The adjusted with the structure of the fiber bundle local coordinates are , , and two coordinates of the vector S. By construction, the structure group transformations leave inert points of the base, 푖 = 0.…”

Section: Advances In Mathematical Physicsmentioning

confidence: 99%

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Recent Progress on the Description of Relativistic Spin: Vector Model of Spinning Particle and Rotating Body with Gravimagnetic Moment in General Relativity

Дериглазов

Ramírez

2017

Advances in Mathematical Physics

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We review the recent results on development of vector models of spin and apply them to study the influence of spin-field interaction on the trajectory and precession of a spinning particle in external gravitational and electromagnetic fields. The formalism is developed starting from the Lagrangian variational problem, which implies both equations of motion and constraints which should be presented in a model of spinning particle. We present a detailed analysis of the resulting theory and show that it has reasonable properties on both classical and quantum level. We describe a number of applications and show how the vector model clarifies some issues presented in theoretical description of a relativistic spin: (A) one-particle relativistic quantum mechanics with positive energies and its relation with the Dirac equation and with relativistic Zitterbewegung; (B) spin-induced noncommutativity and the problem of covariant formalism; (C) three-dimensional acceleration consistent with coordinate-independence of the speed of light in general relativity and rainbow geometry seen by spinning particle; (D) paradoxical behavior of the Mathisson-PapapetrouTulczyjew-Dixon equations of a rotating body in ultrarelativistic limit, and equations with improved behavior.

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Section: Advances In Mathematical Physicsmentioning

confidence: 99%

“…The inclusion of an interaction into the geometry of phase-space and the resulting noncommutative geometry is under intensive investigation in various models [55,95,[97][98][99][100][101][102][103][104][105][106][107][108][109][110][111][112][113][114][115].…”

Section: Parametrization Of Physical Time and Physical Hamiltonian Ementioning

confidence: 99%

Recent Progress on the Description of Relativistic Spin: Vector Model of Spinning Particle and Rotating Body with Gravimagnetic Moment in General Relativity

Дериглазов

Ramírez

2017

Advances in Mathematical Physics

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“…In fact, the momenta p x and p y are special case of the so-called geometric momentum p = −i (∇ surf + M n/2) [6] on an N -dimensional surface which is embedded in (N + 1)-dimensional Euclidean space, where ∇ surf is the gradient operator on surface, and M is the mean curvature and n is the normal vector [6]. The geometric momentum is recently intensively studied [8][9][10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Distribution of x ⋅ p for quantum states on a circle

Liu

Qin

Huang

et al. 2015

Int. J. Geom. Methods Mod. Phys.

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We first give the proper definition of the particle's position-momentum dot product, the so-called posmom x · p, to quantum states on a circular circle, in which the momentum turns out to be the geometric one that is recently intensively studied. Second, we carry out the posmom distributions for eigenstates of the free motion on the circle, i.e. exp(imϕ)/ √ 2π, (m = 0, ±1, ±2, . . .). The results are not only potentially experimentally testable, but also reflect a fact that the embedding of the circle S 1 in two-dimensional flat space R 2 is physically reasonable.

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“…It may not be a shortcoming, though. Instead, the over-description has the remarkable advantage to include the results predicted by the the confining potential technique [2,3,5,16,17,20,[23][24][25]. Thus, from the point of view of the operator algebra, a complete formulation of the quantization of the constrained motion is still an open problem [4,26].…”

Section: Remarks On the Quantization Problem Of The Constrained Motionmentioning

confidence: 99%

“…(1) is purely from intrinsic geometry, from which we know that the Dirac quantization of the constrained systems cannot be fulfilled throughout [17]. On the other hand, Eq.…”

Section: Introductionmentioning

confidence: 99%

The centripetal force law and the equation of motion for a particle on a curved hypersurface

Lian

Liu

2016

Eur. Phys. J. C

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It is pointed out that the current form of the extrinsic equation of motion for a particle constrained to remain on a hypersurface is in fact a half-finished version; for it is established without regard to the fact that the particle can never depart from the geodesics on the surface. Once this fact is taken into consideration, the equation takes the same form as that for the centripetal force law, provided that the symbols are re-interpreted so that the law is applicable for higher dimensions. The controversial issue of constructing operator forms of these equations is addressed, and our studies show the quantization of constrained system based on the extrinsic equation of motion is preferable.

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Can Dirac quantization of constrained systems be fulfilled within the intrinsic geometry?

Cited by 33 publications

References 21 publications

Recent Progress on the Description of Relativistic Spin: Vector Model of Spinning Particle and Rotating Body with Gravimagnetic Moment in General Relativity

Recent Progress on the Description of Relativistic Spin: Vector Model of Spinning Particle and Rotating Body with Gravimagnetic Moment in General Relativity

Distribution of x ⋅ p for quantum states on a circle

The centripetal force law and the equation of motion for a particle on a curved hypersurface

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