Unitarily Equivalent Classes of First Order Differential Operators

Details Unitarily Equivalent Classes of First Order Differential Operators Unitarily Equivalent Classes of First Order Differential Operators

1999-06-07

arxiv.org/abs/math-ph/9906006v2

Physics

Mathematical Physics

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Scientific paper

The elements of the class of non-homogeneous differential operators which are based on the same vector field, when viewed as acting on appropriate Hilbert spaces, are shown to be isomorphic to each other. It shown that the replacement of a non-homogeneous operator by a homogeneous one amouts to appropriately changing the volume element in the manifold. An emphasize is given to the case of symmetric operators and the corresponding quantum momentum observables.

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