Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 7 (2011), 106, 12 pages      arXiv:1111.5409      http://dx.doi.org/10.3842/SIGMA.2011.106

Classical and Quantum Dynamics on Orbifolds

Yuri A. Kordyukov
Institute of Mathematics, Russian Academy of Sciences, 112 Chernyshevsky Str., Ufa 450008, Russia

Received September 04, 2011, in final form November 20, 2011; Published online November 23, 2011

Abstract
We present two versions of the Egorov theorem for orbifolds. The first one is a straightforward extension of the classical theorem for smooth manifolds. The second one considers an orbifold as a singular manifold, the orbit space of a Lie group action, and deals with the corresponding objects in noncommutative geometry.

Key words: microlocal analysis; noncommutative geometry; symplectic reduction; quantization; foliation; orbifold; Hamiltonian dynamics; elliptic operators.

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