Quantum mechanics on manifolds and topological effects

Details Quantum mechanics on manifolds and topological effects Quantum mechanics on manifolds and topological effects

2007-07-23

arxiv.org/abs/0707.3357v2

Lett.Math.Phys.82:219-236,2007

Physics

Mathematical Physics

A few comments have been added to the Introduction, together with related references; a few words have been changed in the Abs

Scientific paper

10.1007/s11005-007-0188-5

A unique classification of the topological effects associated to quantum mechanics on manifolds is obtained on the basis of the invariance under diffeomorphisms and the realization of the Lie-Rinehart relations between the generators of the diffeomorphism group and the algebra of infinitely differentiable functions on the manifold. This leads to a unique ("Lie-Rinehart") C* algebra as observable algebra; its regular representations are shown to be locally Schroedinger and in one to one correspondence with the unitary representations of the fundamental group of the manifold. Therefore, in the absence of spin degrees of freedom and external fields, the first homotopy group of the manifold appears as the only source of topological effects.

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