Quantized fiber dynamics for extended elementary objects involving gravitation

Foundations of Physics 22 (8):1041-1077 (1992)
  Copy   BIBTEX


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 the principal series of unitary irreducible representations determined by the parameter ρ. The bundle ℋ, associated to the de Sitter frame bundle P(B, G), provides a geometric arena with built-in fundamental length parameter R (taken to be of the order of 10−13 cm characterizing hadron physics) yielding, in the presence of gravitation, a quantum kinematical framework for the geometro-stochastic description of spinless matter described in terms of generalized quantum mechanical wave functions, Ψ x ρ (ξ, ζ), defined on #x210B;. By going over to a nonlinear realization of the de Sitter group with the help of a section ξ(x) on the soldered bundle E, associated to P, with homogeneous fiber V′4⋍G/H, one is able to recover gravitation in a de Sitter gauge invariant manner as a gauge theory related to the Lorentz subgroup H of G. ξ(x) plays the dual role of a symmetry-reducing and an extension field. After introducing covariant bilinear source currents in the fields Ψ x ρ (ξ, ζ) and their adjoints determined by G-invariant integration over the local fibers in ℋ, a quantum fiber dynamical (QFD) framework is set up for the dynamics at small distances in B determining the geometric quantities beyond the classical metric of Einstein's theory through a set of current-curvature field equations representing the source equations for axial vector torsion and the de Sitter boost contributions to the bundle connection (the latter defining the soldering forms of the Cartan connection in P(B, G) in the nonlinear gauge). The presented bundle framework yields a theory for quantized material objects in interaction with gravitation, the long-range metrical part of which remains classical



    Upload a copy of this work     Papers currently archived: 74,662

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Modified Weyl Theory and Extended Elementary Objects.W. Drechsler - 1989 - Foundations of Physics 19 (12):1479-1497.
Classical Versus Quantum Gravity.Wolfgang Drechsler - 1993 - Foundations of Physics 23 (2):261-276.
A Gauge Field Theory of Spacetime Based on the de Sitter Group.P. K. Smrz - 1980 - Foundations of Physics 10 (3-4):267-280.
Gravitation Theory in the spacetimeR×S 3.G. Zet, C. Pasnicu & M. Agop - 1991 - Foundations of Physics 21 (4):473-481.
Geometrie Und Materie — Ist Einsteins Vision Übertragbar Auf Die Elementarteilchenphysik?Wolfgang Drechsler - 1984 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 15 (1):1-21.
Relativistic State Reduction Dynamics.Daniel J. Bedingham - 2011 - Foundations of Physics 41 (4):686-704.


Added to PP

12 (#798,201)

6 months
1 (#419,921)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references