The quantum-to-classical transition: contraction of associative products
  The quantum-to-classical transition is considered from the point of view of contractions of associative algebras. Various methods and ideas to deal with contractions of associative algebras are discussed that account for a large family of examples. As an instance of them, the commutative algebra of functions in phase space, corresponding to classical physical observables, is obtained as a contraction of the Moyal star-product which characterizes the quantum case. Contractions of associative algebras associated to Lie algebras are discussed, in particular the Weyl-Heisenberg and $SU(2)$ groups are considered. 
A. Ibort, V.I. Man'ko, G. Marmo, A. Simoni, C. Stornaiolo, F.   Ventriglia
quant-ph math-ph math.MP