The quantum-to-classical transition: contraction of associative products Articles uri icon

publication date

  • April 2016


  • 4


  • 91

International Standard Serial Number (ISSN)

  • 0031-8949

Electronic International Standard Serial Number (EISSN)

  • 1402-4896


  • 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.


  • Mathematics


  • moyal product; classical-to-quantum transition; associative algebras contraction; commutation relations; star products; systems; tomography; duality