English

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}
}