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arXiv · 0707.2708

On the self-adjointness of certain reduced Laplace-Beltrami operators

L. Feher·B. G. Pusztai
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Abstract

The self-adjointness of the reduced Hamiltonian operators arising from the Laplace-Beltrami operator of a complete Riemannian manifold through quantum Hamiltonian reduction based on a compact isometry group is studied. A simple sufficient condition is provided that guarantees the inheritance of essential self-adjointness onto a certain class of restricted operators and allows us to conclude the self-adjointness of the reduced Laplace-Beltrami operators in a concise way. As a consequence, the self-adjointness of spin Calogero-Sutherland type reductions of `free' Hamiltonians under polar actions of compact Lie groups follows immediately.

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L. Feher, B. G. Pusztai. 2007-11-30. On the self-adjointness of certain reduced Laplace-Beltrami operators. https://doi.org/10.1016/s0034-4877(08)00012-8

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