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 unitary operator of formula_103 that commutes with them is an formula_121 multiplier. But commuting with translations implies that the multiplier is constant. A version of the Stone–von Neumann theorem, proved by George Mackey, holds for the Heisenberg group formula_113. The Fourier transform is the unique intertwiner between the representations of formula_103 and formula_124. See the discussion at Stone–von Neumann theorem#Relation to the Fourier transform for details. Heisenberg group In mathematics, the Heisenberg group formula_1, named after Werner Heisenberg, is the group of 3×3 upper triangular matrices of the form under the operation of matrix multiplication. Elements "a, b" and "c"