Quantum integrability of quadratic Killing tensors

Christian Duval (1, 2) , Galliano Valent (3)

1 CPT - E2 Géométrie, Physique et Symétries
2 CPT - Centre de Physique Théorique - UMR 7332
3 LPTHE - Laboratoire de Physique Théorique et Hautes Energies

Quantum integrability of classical integrable systems given by quadratic Killing tensors on curved configuration spaces is investigated. It is proven that, using a "minimal" quantization scheme, quantum integrability is insured for a large class of classic examples.

Mots clés: Classical integrability; geodesic flows; Stäckel systems; quantization; quantum integrability

Domaines: Physique mathématique [math-ph]

Christian Duval, Galliano Valent. Quantum integrability of quadratic Killing tensors. Journal of Mathematical Physics, 2005, 46, pp.053516. ⟨10.1063/1.1899986⟩. ⟨hal-00003609v4⟩