Geometro-differential conception of extended particles and their quantum theory in de Sitter space

Smida, A.; Hachemane, M.; Fellah, M.

doi:10.1007/bf02057888

Cited by 6 publications

(4 citation statements)

References 14 publications

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“…In the strict sense, X[t, u] should be a wave in a space R u containing the physical waves. Since the guidelines for the definition of such a wave are far from being obvious, we have previously [10,17] chosen a simple bilocal form…”

Section: Functional and Stochastic Theoriesmentioning

confidence: 99%

“…In other words, what is important for us is the banishment of the pointlike conception of elementary particles. A geometrodifferential model [10,17] has been constructed on this basis, where the extended particles are composed of two quantum local modes. The external mode evolves in the external physical space-time and the internal mode is localized in an internal space-time, the points of which are arguments of the physical wave u.…”

Section: Introductionmentioning

confidence: 99%

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Stochastically and Intrinsically Extended Non-relativistic Quantum Particles

et al. 2007

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Stochastically and intrinsically extended non relativistic quantum particles are described by combining the ideas of a stochastic quantum theory and a quantum functional theory. The former relates the extension to imperfect real measurements while the latter considers it as intrinsic. Physical states, Positive-Operator-Valued measures connected to measurement, and propagators are given and discussed. The stochastic theory is sufficient when the bilocal field describing the particle has a product form.

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Section: Functional and Stochastic Theoriesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stochastically and Intrinsically Extended Non-relativistic Quantum Particles

et al. 2007

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“…In the scalar case, the parallel transport affects only the variables (q , p ) and ξ by path ordered elements of the Poincaré and de Sitter groups, respectively [10,11] K µ γ η (x, q, p, ξ; x, q , p , ξ ) = K η (q, p; g( )q , g( )p ) µc (ξ, g( R )ξ )…”

Section: Propagation Of the Extended Particle In A Curved Spacetimementioning

confidence: 99%

“…This program began with our proposal of a geometro-differential model in which the extended particle is composed of an external and an internal quantum mode [10,11]. The external mode represents a global (mean) location of the particle in an external spacetime M with points x and the internal mode plays the role of a constituent located in an internal de Sitter spacetime V R 4 with points ξ .…”

Section: Introductionmentioning

confidence: 99%

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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