Geometric formulation of Berezin deformation quantization

• Main Author: R. Roknizadeh
• Format: Article
• Language: English
• Published: Isfahan University of Technology 2002-06-01
• Series: Iranian Journal of Physics Research
• Subjects: Berezin quantization; geometric quantum mechanics; deformation quantization
• Online Access: http://ijpr.iut.ac.ir/browse.php?a_code=A-10-1-167&slc_lang=en&sid=1

  In this paper we try to formulate the Berezin quantization on projective Hilbert space P(H) and use its geometric structure to construct a correspondence between a given classical theory and a given quantum theory. It wil be shown that the star product in berezin quantization is equivalent to the Posson bracket on coherent states manifold M, embodded in P(H), and the Berezin method is used to define a classical limit for geometric quantum mechnics. With this construction to all of the quantum observables are associated their covariant symbols, which form a poisson algebra on P(H) and since the corresponding classical phase space has a natural Poisson structure, the Berezin quantization is then a systematic procedure to relate these tow piosson algebras.