MODULAR ALGEBRAS IN GEOMETRIC-QUANTIZATION

Presented here is a discussion on the connection between geometric qua ntization and algebraic quantization. The former procedure relies on a construction of unitary irreducible representations that starts from co-adjoint orbits and uses polarizations, while the latter depends on the Purely algebraic characterization of unitary irreducible represent ations, which is based on central decompositions of von Neumann algebr as in involutive duality, and their decompositions in terms of maximal Abelian subalgebras. Intermediate stages of these two quantization me thods turn out to be complementary, leading thus to a new characteriza tion of the so-called discrete series representations. (C) 1994 Americ an Institute of Physics.