Non-diagonal Integrable Quadratic Hamiltonians

Abstract:
The talk discusses a class of non-diagonal quadratic Hamiltonians on so(4) and so(3,1) which contains among its 6 integrable cases one with a 6th degree first integral and a superintegrable Hamiltonian. Inhomogeneous generalizations are found for all cases.

This work was done in collaboration with Vladimir Sokolov.