Path Integrals on Euclidean Space Forms

[摘要] In this paper we develop a quantization method for flat compact manifolds based on path integrals. In this method the Hilbert space of holomorphic functions in the complexification of the manifold is used. This space is a reproducing kernel Hilbert space. A definition of the Feynman propagator, based on the reproducing property of this space, is proposed. In the $\mathbb{R}^n$ case the obtained results coincide with the known expressions.

[关键词] path integrals;holomorphic quantization;space forms;reproducing kernel Hilbert spaces