Riemannian exponential and quantization
Abstract
This article continues and completes our previous work [14] J. Phys. Commun. 2 (2018) 025007. First of all, we present two methods of quantization associated with a linear connection given on a differentiable manifold, one of them being the one presented in [14]. The two methods allow quantize functions that come from covariant tensor fields. The equivalence of both is demonstrated as a consequence of a remarkable property of the Riemannian exponential (Theorem 5.1) that, as far as we know, is new to the literature. On the other hand, the extension of the previously mentioned quantization to functions of a very broad type can be carried out by generalizing the method of [14] in terms of fields of distributions.
Cite
@article{arxiv.1801.05183,
title = {Riemannian exponential and quantization},
author = {J Muñoz-Díaz and RJ Alonso-Blanco},
journal= {arXiv preprint arXiv:1801.05183},
year = {2020}
}
Comments
Important changes have been made with respect to the previous version, including 1) An improved demonstration of the equivalence between the two proposed quantizations and 2) A major extension of one of them to a much broader set of functions. The title, the abstract and the introduction have been modified, making them more in line with the new content