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arXiv · hep-th/9906156

Reparametrization Invariance of Path Integrals

H. Kleinert·A. Chervyakov
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Abstract

We demonstrate the reparametrization invariance of perturbatively defined one-dimensional functional integrals up to the three-loop level for a path integral of a quantum-mechanical point particle in a box. We exhibit the origin of the failure of earlier authors to establish reparametrization invariance which led them to introduce, superfluously, a compensating potential depending on the connection of the coordinate system. We show that problems with invariance are absent by defining path integrals as the epsilon-> 0 -limit of 1+ epsilon -dimensional functional integrals.

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H. Kleinert, A. Chervyakov. 1999-06-28. Reparametrization Invariance of Path Integrals. https://doi.org/10.1016/s0370-2693(99)00943-0

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