Perfect discretization of path integrals

Details Perfect discretization of path integrals Perfect discretization of path integrals

2011-10-18

arxiv.org/abs/1110.4051v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

4 pages, 1 figure, based on a talk given at Loops '11, Madrid, to appear in Journal of Physics: Conference Series (JPCS)

Scientific paper

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.

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