Quantum dynamics of non-relativistic particles and isometric embeddings

Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology

Scientific paper

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Revtex, 14 pages

Scientific paper

10.1088/0264-9381/14/2/012

It is considered, in the framework of constrained systems, the quantum dynamics of non-relativistic particles moving on a d-dimensional Riemannian manifold M isometrically embedded in $R^{d+n}$. This generalizes recent investigations where M has been assumed to be a hypersurface of $R^{d+1}$. We show, contrary to recent claims, that constrained systems theory does not contribute to the elimination of the ambiguities present in the canonical and path integral formulations of the problem. These discrepancies with recent works are discussed.

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