The Schwinger Action Principle and the Feynman Path Integral for Quantum Mechanics in Curved Space

Details The Schwinger Action Principle and the Feynman Path Integral for Quantum Mechanics in Curved Space The Schwinger Action Principle and the Feynman Path Integral for Quantum Mechanics in Curved Space

2004-11-25

arxiv.org/abs/hep-th/0411233v1

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, RevTeX 4 preprint style, no figures

Scientific paper

The Feynman path integral approach to quantum mechanics is examined in the case where the configuration space is curved. It is shown how the ambiguity that is present in the choice of path integral measure may be resolved if, in addition to general covariance, the path integral is also required to be consistent with the Schwinger action principle. On this basis it is argued that in addition to the natural volume element associated with the curved space, there should be a factor of the Van Vleck-Morette determinant present. This agrees with the conclusion of an approach based on the link between the path integral and stochastic differential equations.

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