Quantum Mechanics on Manifolds

Details Quantum Mechanics on Manifolds Quantum Mechanics on Manifolds

1993-06-28

arxiv.org/abs/hep-th/9306144v1

Physics

High Energy Physics

High Energy Physics - Theory

34 pages

Scientific paper

A definition of quantum mechanics on a manifold $ M $ is proposed and a method to realize the definition is presented. This scheme is applicable to a homogeneous space $ M = G / H $. The realization is a unitary representation of the transformation group $ G $ on the space of vector bundle-valued functions. When $ H \ne \{ e \} $, there exist a number of inequivalent realizations. As examples, quantum mechanics on a sphere $ S^n $, a torus $ T^n $ and a projective space $ \RP $ are studied. In any case, it is shown that there are an infinite number of inequivalent realizations.

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