Abstract:
We study representation theory of the Weyl relations for infinitely many degrees of freedom. Differentiability of regular representations along rays in the parameter space E suggests to consider smooth structures on E. Switching from representations of CCR to group representations of the associated Heisenberg group over E we develop a framework for smooth representations of the Heisenberg group as an infinite dimensional Lie group. After careful inspection and translation of the necessary differential geometric input for Kirillov's orbit method we are able to construct a large class of smooth representations. These reproduce the Schrödinger representation if E is finite dimensional.
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Received: 10 May 1996 / Accepted: 30 July 1996
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Hörmann, G. Regular Weyl-Systems and Smooth Structures on Heisenberg Groups . Comm Math Phys 184, 51–63 (1997). https://doi.org/10.1007/s002200050052
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DOI: https://doi.org/10.1007/s002200050052