Quantum surfaces, special functions, and the tunneling effect

Details Quantum surfaces, special functions, and the tunneling effect Quantum surfaces, special functions, and the tunneling effect

2001-06-22

arxiv.org/abs/math/0106187v3

Mathematics

Quantum Algebra

51 pages, Latex-file, added remarks

Scientific paper

The notion of quantum embedding is considered for two classes of examples: quantum coadjoint orbits in Lie coalgebras and quantum symplectic leaves in spaces with non-Lie permutation relations. A method for constructing irreducible representations of associative algebras and the corresponding trace formulas over leaves with complex polarization are obtained. The noncommutative product on the leaves incorporates a closed 2-form and a measure which (in general) are different from the classical symplectic form and the Liouville measure. The quantum objects are related to some generalized special functions. The difference between classical and quantum geometrical structures could even occur to be exponentially small with respect to the deformation parameter. That is interpreted as a tunneling effect in the quantum geometry.

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