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

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

2007-07-18

arxiv.org/abs/0707.2708v2

Rep. Math. Phys. 61 (2008) 163-170

Physics

Mathematical Physics

9 pages, minor changes, updated references in v2

Scientific paper

10.1016/S0034-4877(08)00012-8

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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