Bargmann-Fock realization of the noncommutative torus
(2014) Trends in Mathematics — Vol. 32, n° np, p. 39-48 (2014)
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- Abstract
- We give an interpretation of the Bargmann 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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Anzola Kibamba, N., & Bieliavsky, P. (2014). Bargmann-Fock realization of the noncommutative torus. Trends in Mathematics, 32(np), 39-48. https://doi.org/10.1007/978-3-319-06248-8 (Original work published 2014)