Noncommutative geometry and geometric quantization. (English) Zbl 0756.58022

Symplectic geometry and mathematical physics, Proc. Colloq., Aix-en- Provence/ Fr. 1990, Prog. Math. 99, 446-461 (1991).
[For the entire collection see Zbl 0741.00086.]
The paper contains an exposition of a program initiated separately by the author, M. Karasev and S. Zakrewski. The geometric quantization of objects called symplectic groupoids is suggested as a means for relating the symplectic and Poisson manifolds of classical mechanics to noncommutative algebras. These algebras are of fundamental importance in quantum mechanics. They have also become of increasing interest because of their applications to geometry and to certain Hopf algebras called quantum groups.


53D50 Geometric quantization
46L85 Noncommutative topology
46L87 Noncommutative differential geometry
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory


Zbl 0741.00086