The conformally invariant Laplace-Beltrami operator and factor ordering

Michael P. Ryan, Jr.; Alexander V. Turbiner

doi:10.1016/j.physleta.2004.10.021

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The conformally invariant Laplace-Beltrami operator and factor ordering

Michael P. Ryan, Jr.·Alexander V. Turbiner

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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.

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Michael P. Ryan, Jr., Alexander V. Turbiner. 2004-10-21. The conformally invariant Laplace-Beltrami operator and factor ordering. https://doi.org/10.1016/j.physleta.2004.10.021

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