An invitation to the algebra of canonical commutation relations

Konrad Schmüdgen

Gennadi Aleksandrovich Sardanashvily

Mauro Spera

Huzihiro Araki

F. J. Bloore, J. Underhill

The authors present an algebraic argument which shows that the coordinate free canonical commutation relations of Segal are the natural extension of the coordinate-velocity commutation relations. They do not invoke the Schrodinger representation. They define an algebra of quantum observables for any manifold and show it becomes the usual algebra when the manifold is riemannian.

Hendrik Grundling