Geometro-stochastic quantization of a theory for extended elementary objects |
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Authors: | Wolfgang Drechsler Eduard Prugovečki |
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Affiliation: | (1) Max-Planck-Institut für Physik und Astrophysik, Werner-Heisenberg-Institut für Physik, P.O. Box 40 12 12, Munich, Germany;(2) Department of Mathematics, University of Toronto, M5S 1A1 Toronto, Canada |
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Abstract: | 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 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 is a resolution kernel Hilbert space constructed in terms of generalized coherent states related to the principal series of unitary irreducible representations of SO(4, 1), namely de Sitter horospherical waves for spinless particles characterized by the parameter . The framework is, finally, extended to a quantum field-theoretical formalism by using bundles with Fock space fibers constructed from .Supported in part by NSERC Research Grant No. A5206. |
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