Bargmann–Fock Realization of the Noncommutative Torus

  • Nestor Anzola Kibamba
  • Pierre BieliavskyEmail author
Conference paper
Part of the Trends in Mathematics book series (TM)


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.


Non-commutative torus Bargmann transform Heisenberg group Fock space deformation quantization noncommutative geometry Heisenberg group Bargmann–Segal transform 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Institut de recherche en mathématique et physiqueUniversité catolique de LouvainLouvainBelgium

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