Stochastically and Intrinsically Extended Non-relativistic Quantum Particles

Smida, A.; Hachemane, M.; Hamici, A.-H.; Oualili, Y.

doi:10.1007/s10773-007-9588-7

Cited by 1 publication

(2 citation statements)

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“…In order to arrive at concrete applications of the present work, one can first test the basic idea of adopting a stochastic representation for the external mode and a pointlike representation for the internal mode in the nonrelativistic regime. We have obtained acceptable probability interpretation in that (nongeometrical) case, albeit in a general formulation [21].…”

Section: Discussionmentioning

confidence: 80%

“…whose base manifold is M and the typical fibre is the Hilbert space L 2 × V R 4 carrying the external Poincaré group phase space representation and the internal de Sitter group configuration representation. The direct product representation Û = U(a, l) ⊗ U D (g), ( Û x )(q, p, ξ) = x (l −1 (q − a), l −1 p, g −1 ξ) (21) constitutes the structural group. The inner product is…”

Section: The Fibre Bundles and The Connectionmentioning

confidence: 99%

See 1 more Smart Citation

Intrinsically extended stochastic particles with internal de Sitter symmetry

Benrabia¹,

Hachemane²,

Smida³

et al. 2008

J. Phys. A: Math. Theor.

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We give the propagation of extended particles in a generic curved spacetime. The extended particle may be a scalar system of two quarks viewed as two quantum modes. Precisely, the first mode represents the global location of the extended particle in the curved spacetime and is quantized by the geometro-stochastic method which seems to be well suited for that purpose. The other mode, which represents a relative motion and is naturally confined in a de Sitter internal spacetime, is quantized by the method of induced representations. This corresponds to the relativistic harmonic oscillator in which the interaction has been replaced by a curvature of the internal space (relativistic rotator). States of the extended particle are then defined in a Hilbert bundle structure with the direct product of the external Poincaré and internal de Sitter symmetries playing the role of the structural group. Intertwining operators are used to define propagation in one fibre as a transition amplitude between the so-called local quantum frames. Parallel transport of these frames is used to define the total propagation of the extended particle as advocated by the geometro-stochastic theory.

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Section: Discussionmentioning

confidence: 80%

Section: The Fibre Bundles and The Connectionmentioning

confidence: 99%