The conformally invariant Laplace-Beltrami operator and factor ordering
arXiv:quant-ph/0406167 · doi:10.1016/j.physleta.2004.10.021
Abstract
In quantum mechanics the kinetic energy term for a single particle is usually written in the form of the Laplace-Beltrami operator. This operator is a factor ordering of the classical kinetic energy. We investigate other relatively simple factor orderings and show that the {\it only} other solution for a conformally flat metric is the conformally invariant Laplace-Beltrami operator. For non-conformally-flat metrics this type of factor ordering fails, by just one term, to give the conformally invariant Laplace-Beltrami operator.
7 pages, extra paraghraph and two references are added
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