XXII WORKSHOP ON GEOMETRIC METHODS IN PHYSICS

29 JUNE - 5 JULY 2003, BIAŁOWIEŻA, POLAND

Andrei Shafarevich - Semiclassical quantization of real and complex isotropic manifolds

Theory of semiclassical quantization describes connections between topological characteristics of invariant sets of classical Hamiltonian systems and spectral properties of the corresponding partial differential or pseudodifferential operators. In the lecture we describe briefly the main steps and the modern state of the theory, including recent results. The main aim of the talk is to show how geometrical and topological theory of real and complex isotropic varieties can be used in the problems of description of coherent states, quantum Calogero - Strocci systems, splitting of energy levels, etc.