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arXiv · 1512.06407

Notes on Feynman path integral-like methods of quantization on Riemannian manifolds

Yoshihisa Miyanishi
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Abstract

We propose an alternative method for Feynman path integrals on compact Riemannian manifolds. Our method employs action integrals along the shortest paths. In the case of rank 1 locally symmetric Riemannian manifolds, we prove the strong convergence of time slicing products of oscillatory integrals for low energy functions. Moreover, the strong limit includes Dewitt curvature $R/6$, where $R$ denotes the scalar curvature of a Riemannian manifold.

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Yoshihisa Miyanishi. 2015-12-20. Notes on Feynman path integral-like methods of quantization on Riemannian manifolds. https://arxiv.org/abs/1512.06407

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