Perfect discretization of path integrals

Preprint English OPEN
Steinhaus, Sebastian (2011)

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.
  • References (9)

    [1] http://loops11.iem.csic.es/loops11/index.php?option=com_content&view=article&id=75&Itemid=73

    [2] Bahr B and Dittrich B 2009 (Broken) Gauge Symmetries and Constraints in Regge Calculus Class. Quant. Grav. 26 225011. (Preprint arXiv:0905.1670 [gr-qc]).

    [3] Bahr B, Dittrich B and Steinhaus S 2011 Perfect discretization of reparametrization invariant path integrals Phys. Rev. D83 105026. (Preprint arXiv:1101.4775 [gr-qc]).

    [4] Hasenfratz P and Niedermayer F 1994 Perfect lattice action for asymptotically free theories Nucl. Phys. B414 785-814. (Preprint hep-lat/9308004).

    [5] Marsden J E and West M 2001 Discrete mechanics and variational integrator Acta Numerica , 10 357-514.

    [6] Rocek M and Williams R M 1981 Quantum Regge Calculus Phys. Lett. B104 31.

    [7] Bahr B and Dittrich B 2009 Improved and Perfect Actions in Discrete Gravity Phys. Rev. D80 124030. (Preprint arXiv:0907.4323 [gr-qc]).

    [8] Dittrich B, Eckert F C and Martin-Benito M 2011 Coarse graining methods for spin net and spin foam models Preprint arXiv:1109.4927 [gr-qc].

    [9] Dittrich B and Steinhaus S to appear

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