Alladi Ramakrishnan Hall

Geometric quantization and Lagrangian geometry - Part II

Nikolai Tyurin

BLTPh, JINR (Dubna) and HSE (Moscow)

I would like to present short survey on a lagrangian approach to
Quantization problem, which generalizes classical WKB method and Maslov
semiclassical approximation. The programme is the following

1. Classical methods of Geometric Quantization: Konstant, Suriou, Berezin.

2. Geometric formulation of Quantum Mechanics, proposed by Ashtekar.
Agebro - Geometric quantization.

3. Abelian lagrangian geometry: the moduli space of half weighted Bohr -
Sommerfeld cycles as the quantum phase space of Lagrangian quantization.