Path Integrals on Euclidean Space Forms

Symmetry Integrability and Geometry-Methods and Applications

article

Guillermo Capobianco¹  Walter Reartes¹ 

[1] Universidad Nacional del Sur

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

DOI  :  10.3842/SIGMA.2015.071

来源: National Academy of Science of Ukraine

【 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.

【 授权许可】

Unknown