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

2015/12/20 by Yoshihisa Miyanishi, Miyanishi, Yoshihisa
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1512.06407

arXiv admin note: text overlap with arXiv:1310.1631

arxiv created 2015/12/20 · arxiv updated 2015/12/22

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.

Citations

• Remarks on low-energy approximations for Feynman path integration on the sphere

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