1995/10/04 by Eduard Prugovecki
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Gauge (firearms) #Gauge theory #General covariance #Hilbert space #Invariant (physics) #Noncommutative and Quantum Gravity Theories #Poincaré conjecture #Propagator #Quantum field theory in curved spacetime #Spacetime #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/13/5/017
published as Class.Quant.Grav. 13 (1996) 1007-1022 · Converted from a Mac-Word file to postscript for submission. The author may be reached directly via the above address, or at: [email protected]
arxiv created 1995/10/04 · openalex publication_date 1996/05/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The basic properties of Poincaré 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 Poincaré 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.