Abstract
This chapter describes the quantization in kinematics. In quantum kinematics, there exist many quantization schemes. A common basis of all these methods is an assumption that classical and quantum kinematical structures are different representations of the same totality of mathematical structures. This is the Dirac's correspondence principle. A quantization in kinematics is a general rule that assigns a quantum observable A(Q, P) to each classical observable A(q, p), which is a function on the phase space. It is suggested if algebraic operations for quantum observables are defined, then an algebra of observables are determined by generators. Each element of this algebra can be derived by the application of algebraic operations to generators. Heisenberg kinematical representation, Weyl system and Weyl algebra, and Weyl quantization mapping is also discussed in the chapter.
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