arXiv subjects

Eduard Prugovecki

Publications and source records attributed to Eduard Prugovecki.

3 recordsLinked to original sources

arXiv1996

On Locality in Quantum General Relativity and Quantum Gravity

The physical concept of locality is first analyzed in the special relativistic quantum regime, and compared with that of microcausality and the local commutativity of quantum fields. Its extrapolation to quantum general relativity on quantum bundles over curved spacetime is then described. It is shown that the resulting formulation of quantum-geometric locality based on the concept of local quantum frame incorporating a fundamental length embodies the key geometric and topological aspects of this concept. Taken in conjunction with the strong equivalence principle and the path-integral formulation of quantum propagation, quantum-geometric locality leads in a natural manner to the formulation of quantum-geometric propagation in curved spacetime. Its extrapolation to geometric quantum gravity formulated over quantum spacetime is described and analyzed.

gr-qc↗

arXiv1995

Quantum Geometry and Gravity

The geometro-stochastic method of quantization provides a framework for quantum general relativity, in which the principal frame bundles of local Lorentz frames that underlie the fibre-theoretical approach to classical general relativity are replaced by Poincaré-covariant quantum frame bundles. In the semiclassical regime for quantum field theory in curved spacetime, where the gravitational field is not quantized, the elements of these local quantum frames are generalized coherent states, which emerge naturally from phase space representations of the Poincaré group. Due to their informational completeness, these quantum frames are capable of taking over the role played by complete sets of observables in conventional quantum theory. The propagation of quantum-geometric fields proceeds by path integral methods, based on parallel transport along broken paths consisting of arcs of geodesics of the Levi-Civita connection. The formulation of quantum gravity within this framework necessitates the transition to quantum superframe bundles and a quantum gravitational supergroup capable of incorporating diffeomorphism invariance into the framework. This results in a geometric version of quantum gravity which shares some conceptual features with covariant as well as with canonical gravity, but which avoids the foundational and the mathematical difficulties encountered by these two approaches.

gr-qc↗

arXiv1995

On Quantum-Geometric Connections and Propagators in Curved Spacetime

The basic properties of Poincare gauge invariant Hilbert bundles over Lorentzian manifolds are derived. Quantum connections are introduced in such bundles, which govern a parallel transport that is shown to satisfy the strong equivalence principle in the quantum regime. Path-integral expressions are presented for boson propagators in Hilbert bundles over globally hyperbolic curved spacetimes. Their Poincare gauge covariance is proven, and their special relativistic limit is examined. A method for explicitly computing such propagators is presented for the case of cosmological models with Robertson-Walker metric.

gr-qc↗