Editing Poisson bracket (section)

==Quantization==
Poisson brackets [[Deformation theory|deform]] to [[Moyal bracket]]s upon [[Weyl quantization|quantization]], that is, they generalize to a different Lie algebra, the [[Moyal bracket|Moyal algebra]], or, equivalently in [[Hilbert space]], quantum [[commutator]]s. The Wigner-İnönü [[group contraction]] of these (the classical limit, {{math|ħ → 0}})  yields the above Lie algebra.

To state this more explicitly and precisely, the [[universal enveloping algebra]] of the [[Heisenberg algebra]] is the [[Weyl algebra]] (modulo the relation that the center be the unit). The Moyal product is then a special case of the star product on the algebra of symbols. An explicit definition of the algebra of symbols, and the star product is given in the article on the [[universal enveloping algebra]].