Some instructive examples of quantization

L.D. Faddeev

Steklov Mathematical Institute, Fontanka 27
RU-191911 St. Petersburg, Russia

Abstract:

The term "quantization" has several different meanings. The most general interpretation is connected with the construction of non commutative analogue of classical phase space. In more narrow sence it means a construction of a concrete quantum dynamical model, when its classical analogue is given. In my lectures I shall deal with the latter case. I plan to discuss the questions, which appear in quantization of field-theoretical models on the discretized space time. Here the usual Heisenberg-type canonical variables give way to the Weyl-type ones. We shall see, how this influences the structure of algebra of observables and construction of  concrete relevant operators, such as evolution operator. As an example, the discretized version of the Liouville model will be considered.