The Conformal Group SU(2,2) and Integrable Systems on a Lorentzian Hyperboloid

Details The Conformal Group SU(2,2) and Integrable Systems on a Lorentzian Hyperboloid The Conformal Group SU(2,2) and Integrable Systems on a Lorentzian Hyperboloid

1994-07-15

arxiv.org/abs/hep-th/9407080v1

Fortsch.Phys.44:199-233,1996

Physics

High Energy Physics

High Energy Physics - Theory

37 pages (CRM 2194)

Scientific paper

Eleven different types of "maximally superintegrable" Hamiltonian systems on the real hyperboloid $(s^0)^2-(s^1)^2+(s^2)^2-(s^3)^2=1$ are obtained. All of them correspond to a free Hamiltonian system on the homogeneous space $SU(2,2)/U(2,1)$, but to reductions by different maximal abelian subgroups of $SU(2,2)$. Each of the obtained systems allows 5 functionally independent integrals of motion, from which it is possible to form two or more triplets in involution (each of them includes the hamiltonian). The corresponding classical and quantum equations of motion can be solved by separation of variables on the $O(2,2)$ space.

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