the noncommutative star-multiplication characterizing quantum mechanics and underlying its uncertainty principle. Despite its name, usually Deformation Quantization does not constitute a successful quantization scheme, namely a method to produce a quantum theory out of a classical one. Nowadays, it amounts to a mere representation change from Hilbert space to phase space. Generalizations In more generality, Weyl quantization is studied in cases where the phase space is a symplectic manifold, or possibly a Poisson manifold. Related structures include the Poisson–Lie groups and Kac–Moody algebras. See also Canonical commutation relation Heisenberg group Moyal bracket Weyl algebra Functor Pseudo-differential operator Wigner quasi-probability distribution Stone–von Neumann theorem Phase space formulation of quantum mechanics Kontsevich quantization formula Gabor–Wigner transform Oscillator representation References Further reading (Sections I to IV of this article provide an overview over the Wigner–Weyl transform, the Wigner quasiprobability distribution, the phase space formulation of quantum mechanics and the example of the quantum harmonic oscillator.) Terence Tao's 2012 notes on Weyl ordering Mathematical quantization Mathematical physics Foundational quantum physics Concepts in physics