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The Conformal Group SU (2, 2) and Integrable Systems on a Lorentzian Hyperboloid
Author(s) -
del Olmo M. A.,
Rodríguez M. A.,
Winternitz P.
Publication year - 1996
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190440303
Subject(s) - hyperboloid , integrable system , conformal map , mathematical physics , hamiltonian (control theory) , hamiltonian system , mathematics , homogeneous , pure mathematics , quantum , physics , mathematical analysis , classical mechanics , quantum mechanics , geometry , combinatorics , mathematical optimization
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.