Dependence of the affine coherent states quantization on the parametrization of the affine group
Abstract
The affine coherent states quantization is a promising integral quantization of Hamiltonian systems when the phase space includes at least one conjugate pair of variables which takes values from a half-plane. Such a situation is common for gravitational systems which include singularities. The construction of the quantization map includes a one-to-one mapping of the half-plane onto the affine group. Particular cases of this mapping define specific parametrizations of the group. Our aim is showing that different such parametrizations lead to unitarily inequivalent quantum theories. Depending on the Hamiltonian system under consideration, this dependence could potentially be used constructively.
Keywords
Cite
@article{arxiv.1908.10039,
title = {Dependence of the affine coherent states quantization on the parametrization of the affine group},
author = {Andrzej Góźdź and Włodzimierz Piechocki and Tim Schmitz},
journal= {arXiv preprint arXiv:1908.10039},
year = {2020}
}
Comments
13 pages, no figures, version accepted for publication in European Physical Journal Plus