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Coordinate free canonical commutation relations

F J Bloore and J Underhill

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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.


PACS

03.65.Fd Algebraic methods

02.40.Ky Riemannian geometries

MSC

81Qxx General mathematical topics and methods in quantum theory

81Rxx Groups and algebras in quantum theory

Subjects

Mathematical physics

Quantum information and quantum mechanics

Dates

Issue 7 (1 July 1973)



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