A fibre bundle formulation of quantum geometry

Quantum geometries whose points are stochastic and serve as seats for quantum space-time excitons are formulated as fibre bundles over base spaces of mean values with a Minkowski or general relativistic structure. The fibres contain the proper wave functions of all exciton states in a given model. The notion of covariance and propagation in quantum space-times constituting such fibre bundles is investigated. Maxwell and Yang-Mills gauge degrees of freedom are introduced by appropriately enlarging the structure group, which in all cases contains phase-space representations of the Poincare group corresponding to the exciton wave function sample space specific to a given model. It is shown that these formulations give rise in a natural manner to certain realizations of the relativistic canonical commutation relations in terms of covariant derivatives involving internal as well as external degrees of freedom of space-time excitons