Berezin F A General Concept Of Quantization英文电子书.pdf

Commun. math . Phys . 40, 153—174 (1975) © by Springer-Verlag 1975 General Concept of Quantization F. A. Berezin* Academy of Sciences of the Ukrainian SSR, Institute for Theoretical Physics, Kiev, Ukrainian, SSR Received Jun e 15, 1974 Abstract. The general definition of quantization is proposed . As an example two classical systems are considered. For the first of them the phase space is a Lobachevskii plane, for the second one the two-dimensional sphere. It is generally accepted that the quantization is an algorithm by means of which a quantum system corresponds to a classical dynamic one. Furthermore, it is required that in the limit ft-0 where h is the Plancks constant, a quantum dynamic system change to a corresponding classical one. This requirement is called the . correspondence principle. It is quite obvious that there exist quite a lot quantizations obeying the correspondence principle ; the quantum description of a physical phenomenon is more detailed than the classical one, and so there are certain phenomena the difference between which is displayed in their quantum description, whereas their classical description does not show this difference. The following intuitive method of quantizing the classical dynamic systems with a flat phase space has become well known since the