Quantized Matter in a De Sitter Gauge Theorywith Classical Metric and Axial Torsion

The dualism between classical matter and geometry is extended to include elementary hadronic matter described in quantized form in terms of a gauge theory based on the group SO(4; 1) containing a built-in fundamental length parameter R of geometric origin of the order of a Fermi. Quantized matter at subnuclear distances is described in terms of generalized quantum mechanical wave functions ((rst quantized geometro-stochastically quantized elds) which are identiied with sections on a soldered Hilbert bundle H with Cartan connection constructed over a curved Riemann-Cartan space-time base. The bundle H carries a unitary irre-ducible spin zero phase space representation of the de Sitter group, i.e. a system of covariance of SO(4; 1) describing elementary objects extended at a scale of length given by R. The Lorentz subgroup of SO(4; 1) is related to a vierbein formulation of gravitation. Two sets of source equations for the underlying Riemann-Cartan geometry are considered: (i) Einstein-type equations and (ii) current-curvature equations of Yang-Mills type relating the energy-momentum and SO(4; 1)-gauge current distributions of classical as well as quantized matter to the underlying geometry. It is shown that Einstein's metric theory of gravitation is contained in this scheme as an unquantized classical theory embedded in a geometric framework involving {besides classical macrophysical sources { quantized microphysical material sources determining quantum eeects for the additional nonmetric elds of the geometry (torsion) which are induced at small distances by that part of matter described in a quantum mechanical manner. Axial vector torsion is considered explicitly and a set of nonlinear eld equations for the axial vector torsion eld is derived from the current-curvature equations.