The conformally invariant Laplace-Beltrami operator and factor ordering

Details The conformally invariant Laplace-Beltrami operator and factor ordering The conformally invariant Laplace-Beltrami operator and factor ordering

2004-06-23

arxiv.org/abs/quant-ph/0406167v2

Phys.Lett. A333 (2004) 30-34

Physics

Quantum Physics

7 pages, extra paraghraph and two references are added

Scientific paper

10.1016/j.physleta.2004.10.021

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.

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