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

A. Smida, M. Hachemane & M. Fellah

Foundations of Physics 25 (12):1769-1795 (1995)

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The stochastic quantum mechanics approach to the unification of relativity and quantum theory.E. Prugovečki - 1984 - Foundations of Physics 14 (12):1147-1162.details The stochastic phase-space solution of the particle localizability problem in relativistic quantum mechanics is reviewed. It leads to relativistically covariant probability measures that give rise to covariant and conserved probability currents. The resulting particle propagators are used in the formulation of stochastic geometries underlying a concept of quantum spacetime that is operationally based on stochastically extended quantum test particles. The epistemological implications of the intrinsic stochasticity of such quantum spacetime frameworks for microcausality, the EPR paradox, etc., are discussed. Download Export citation Bookmark 3 citations
Quantized fiber dynamics for extended elementary objects involving gravitation.W. Drechsler - 1992 - Foundations of Physics 22 (8):1041-1077.details The geometro-stochastic quantization of a gauge theory for extended objects based on the (4, 1)-de Sitter group is used for the description of quantized matter in interaction with gravitation. In this context a Hilbert bundle ℋ over curved space-time B is introduced, possessing the standard fiber ℋ $_{\bar \eta }^{(\rho )} $ , being a resolution kernel Hilbert space (with resolution generator $\tilde \eta $ and generalized coherent state basis) carrying a spin-zero phase space representation of G=SO(4, 1) belonging to (...) Download Export citation Bookmark 2 citations
Modified Weyl theory and extended elementary objects.W. Drechsler - 1989 - Foundations of Physics 19 (12):1479-1497.details To represent extension of objects in particle physics, a modified Weyl theory is used by gauging the curvature radius of the local fibers in a soldered bundle over space-time possessing a homogeneous space G/H of the (4, 1)-de Sitter group G as fiber. Objects with extension determined by a fundamental length parameter R0 appear as islands D(i) in space-time characterized by a geometry of the Cartan-Weyl type (i.e., involving torsion and modified Weyl degrees of freedom). Farther away from the domains (...) Download Export citation Bookmark 2 citations
Geometro-stochastic quantization of a theory for extended elementary objects.Wolfgang Drechsler & Eduard Prugovečki - 1991 - Foundations of Physics 21 (5):513-546.details The geometro-stochastic quantization of a gauge theory based on the (4,1)-de Sitter group is presented. The theory contains an intrinsic elementary length parameter R of geometric origin taken to be of a size typical for hadron physics. Use is made of a soldered Hilbert bundle ℋ over curved spacetime carrying a phase space representation of SO(4, 1) with the Lorentz subgroup related to a vierbein formulation of gravitation. The typical fiber of ℋ is a resolution kernel Hilbert space ℋ $_{\bar (...) Download Export citation Bookmark 5 citations
Currents in a theory of strong interaction based on a fiber bundle geometry.W. Drechsler - 1977 - Foundations of Physics 7 (9-10):629-671.details A fiber bundle constructed over spacetime is used as the basic underlying framework for a differential geometric description of extended hadrons. The bundle has a Cartan connection and possesses the de Sitter groupSO(4, 1) as structural group, operating as a group of motion in a locally defined space of constant curvature (the fiber) characterized by a radius of curvatureR≈10−13 cm related to the strong interactions. A hadronic matter field ω(x, ζ) is defined on the bundle space, withx the spacetime coordinate (...) Download Export citation Bookmark 5 citations

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