On the self-adjointness of certain reduced laplace-beltrami operators

L. Fehér, B. G. Pusztai

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)163-170
Number of pages8
JournalReports on Mathematical Physics
Volume61
Issue number2
DOIs
Publication statusPublished - Apr 2008

Fingerprint

Self-adjointness
Laplace-Beltrami Operator
operators
Polar Actions
Essential Self-adjointness
Isometry Group
Compact Lie Group
Compact Group
Operator
Immediately
Riemannian Manifold
Sufficient Conditions

Keywords

  • Hamiltonian reduction
  • integrable systems
  • polar action
  • self-adjointness

ASJC Scopus subject areas

  • Mathematical Physics
  • Statistical and Nonlinear Physics

Cite this

On the self-adjointness of certain reduced laplace-beltrami operators. / Fehér, L.; Pusztai, B. G.

In: Reports on Mathematical Physics, Vol. 61, No. 2, 04.2008, p. 163-170.

Research output: Contribution to journalArticle

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