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.
CITATION STYLE
Kibamba, N. A., & Bieliavsky, P. (2014). Bargmann-Fock realization of the noncommutative torus. In Trends in Mathematics (Vol. 64, pp. 39–48). Springer International Publishing. https://doi.org/10.1007/978-3-319-06248-8_3
Mendeley helps you to discover research relevant for your work.