Invariant classification of orthogonally separable Hamiltonian systems in Euclidean space

DOI10.1007/s00220-005-1331-8zbMath1088.37029arXivmath-ph/0605023OpenAlexW3100709352MaRDI QIDQ818592

Roman G. Smirnov, Joshua T. Horwood, Raymond G. Mclenaghan

Publication date: 21 March 2006

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0605023

zbMATH Keywords

integrabilityKilling tensorsHamiltonian systems on \(\mathbb{E}^{3}\)orthogonal coordinate webs

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Groups and algebras in quantum theory and relations with integrable systems (81R12) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45)

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Cites Work

• Killing tensors as irreducible representations of the general linear group
• The super-separability of the three-body inverse-square Calogero system
• Covariants, joint invariants and the problem of equivalence in the invariant theory of Killing tensors defined in pseudo-Riemannian spaces of constant curvature
• Killing tensors in spaces of constant curvature
• Group invariant classification of separable Hamiltonian systems in the Euclidean plane and the O(4)-symmetric Yang–Mills theories of Yatsun
• An extension of the classical theory of algebraic invariants to pseudo-Riemannian geometry and Hamiltonian mechanics
• Ricci-Calculus
• Killing tensor fields on spaces of constant curvature
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