Quantization (physics) attempts to carry out quantization, for which there is in general no exact recipe, in such a way that certain analogies between the classical theory and the quantum theory remain manifest. For example, the similarity between the Heisenberg equation in the Heisenberg picture of quantum mechanics and the Hamilton equation in classical physics should be built in. One of the earliest attempts at a natural quantization was Weyl quantization, proposed by Hermann Weyl in 1927. Here, an attempt is made to associate a quantum-mechanical observable (a self-adjoint operator on a Hilbert space) with a real-valued function on classical phase space.
Heisenberg group a group, as is shown by the multiplication: and The Heisenberg group is a simply-connected Lie group whose Lie algebra consists of matrices where By letting e, ..., e be the canonical basis of R, and setting the associated Lie algebra can be characterized by the canonical commutation relations, where "p", ..., "p", "q", ..., "q", "z" are the algebra generators. In particular, "z" is a "central" element of the Heisenberg Lie algebra. Note that the Lie algebra of the Heisenberg group is nilpotent. The exponential map is given by the following expression The exponential map of a nilpotent Lie