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arXiv · 1311.0481

Bargmann-Fock realization of the noncommutative torus

Nestor Anzola Kibamba·Pierre Bieliavsky
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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.

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Nestor Anzola Kibamba, Pierre Bieliavsky. 2013-11-03. Bargmann-Fock realization of the noncommutative torus. https://arxiv.org/abs/1311.0481

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