2011/10/18 by Sebastian Steinhaus
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Black Holes and Theoretical Physics #Computer science #Diffeomorphism #Discretization #General relativity #Geometry #Homogeneous space #Mathematical analysis #Mathematical physics #Mathematics #Numerical methods for differential equations #Path (computing) #Path integral formulation #Physics #Pure mathematics #Quantum mechanics #Symmetry (geometry) #gr-qc #hep-lat
paper · pdf · doi:10.1088/1742-6596/360/1/012025
published as J. Phys.: Conf. Ser. 360 012025 (2012) · 4 pages, 1 figure, based on a talk given at Loops '11, Madrid, to appear in Journal of Physics: Conference Series (JPCS)
arxiv created 2011/10/18 · openalex publication_date 2012/05/16 · arxiv updated 2012/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In order to obtain a well-defined path integral one often employs discretizations. In the case of General Relativity these generically break diffeomorphism symmetry, which has severe consequences since these symmetries determine the dynamics of the corresponding system. In this article we consider the path integral of reparametrization invariant systems as a toy example and present an improvement procedure for the discretized propagator. Fixed points and convergence of the procedure are discussed. Furthermore we show that a reparametrization invariant path integral implies discretization independence and acts as a projector onto physical states.