A Convergent Star Product on the Poincar\'e Disc
Complex Variables
2021-08-20 v1 Functional Analysis
Operator Algebras
Quantum Algebra
Abstract
On the Poincar\'e disc and its higher-dimensional analogs one has a canonical formal star product of Wick type. We define a locally convex topology on a certain class of real-analytic functions on the disc for which the star product is continuous and converges as a series. The resulting Fr\'echet algebra is characterized explicitly in terms of the set of all holomorphic functions on an extended and doubled disc of twice the dimension endowed with the natural topology of locally uniform convergence. We discuss the holomorphic dependence on the deformation parameter and the positive functionals and their GNS representations of the resulting Fr\'echet algebra.
Keywords
Cite
@article{arxiv.1803.02763,
title = {A Convergent Star Product on the Poincar\'e Disc},
author = {Daniela Kraus and Oliver Roth and Matthias Schötz and Stefan Waldmann},
journal= {arXiv preprint arXiv:1803.02763},
year = {2021}
}