Bargmann-Fock realization of the noncommutative torus
Quantum Algebra
2013-11-05 v1
Abstract
We give an interpretation of the Bargman transform as a correspondence between state spaces that is analogous to commonly considered intertwiners in representation theory of finite groups. We observe that the non-commutative torus is nothing else that the range of the star-exponential for the Heisenberg group within the Kirillov's orbit method context. We deduce from this a realization of the non-commutative torus as acting on a Fock space of entire functions.
Keywords
Cite
@article{arxiv.1311.0481,
title = {Bargmann-Fock realization of the noncommutative torus},
author = {Nestor Anzola Kibamba and Pierre Bieliavsky},
journal= {arXiv preprint arXiv:1311.0481},
year = {2013}
}