Abstract
We introduce an associative bilinear product F * G on the space of Schwartz functions of the coadjoint orbits \(\mathcal{O}_\lambda \) of a large family of nilpotent Lie groups. We can then introduce an operator
, for all
. When the nilpotent group is the Heisenberg group N(3), the correspondence \(F \mapsto \tilde T(F)\) is a canonical prequantization of functions F(q, p) in phase space.
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References
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Part of this work was done at the University of California, Los Angeles.
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Lugo, V.A. An associative algebra of functions on the orbits of nilpotent Lie groups. Lett Math Phys 5, 509–516 (1981). https://doi.org/10.1007/BF00408132
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DOI: https://doi.org/10.1007/BF00408132