Path Integrals on Euclidean Space Forms

Abstract

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.

References in corpus (2)

• Topology and the Cosmic Microwave Background
• Wick Quantization of Cotangent Bundles over Riemannian Manifolds

Cited by in corpus (1)

• Holomorphic Path Integrals in Tangent Space for Flat Manifolds