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dc.contributor.authorBoyer, C.P.
dc.contributor.authorKalnins, Ernie G.
dc.contributor.authorWinternitz, P.
dc.date.accessioned2008-10-31T03:18:54Z
dc.date.available2008-10-31T03:18:54Z
dc.date.issued1983-08
dc.identifier.citationBoyer, C.P., Kalnins, E.G. & Winternitz, P. (1983). Completely integrable relativistic Hamiltonian systems and separation of variables in Hermitian hyperbolic spaces. Journal of Mathematical Physics, 24, 2022.en_US
dc.identifier.issn0022-2488
dc.identifier.urihttps://hdl.handle.net/10289/1225
dc.description.abstractThe Hamilton–Jacobi and Laplace–Beltrami equations on the Hermitian hyperbolic space HH(2) are shown to allow the separation of variables in precisely 12 classes of coordinate systems. The isometry group of this two-complex-dimensional Riemannian space, SU(2,1), has four mutually nonconjugate maximal abelian subgroups. These subgroups are used to construct the separable coordinates explicitly. All of these subgroups are two-dimensional, and this leads to the fact that in each separable coordinate system two of the four variables are ignorable ones. The symmetry reduction of the free HH(2) Hamiltonian by a maximal abelian subgroup of SU(2,1) reduces this Hamiltonian to one defined on an O(2,1) hyperboloid and involving a nontrivial singular potential. Separation of variables on HH(2) and more generally on HH(n) thus provides a new method of generating nontrivial completely integrable relativistic Hamiltonian systems.en_US
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.relation.urihttp://link.aip.org/link/?JMAPAQ/24/2022/1en_US
dc.rightsCopyright 1983 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in the Journal of Mathematical Physics and may be found at http://jmp.aip.org/jmp/top.jspen_US
dc.subjectMathematicsen_US
dc.subjectHamilton&minusen_US
dc.subjectJacobi equationsen_US
dc.subjectlaplace equationen_US
dc.subjectmathematical spaceen_US
dc.subjectcoordinatesen_US
dc.subjectRiemann spaceen_US
dc.subjectSU groupsen_US
dc.subjectHamiltoniansen_US
dc.subjectsymmetryen_US
dc.subjecthermitian operatorsen_US
dc.subjectinvariance principlesen_US
dc.subjectintegrable systemsen_US
dc.subjectrelativistic rangeen_US
dc.subjectalgebrasen_US
dc.subjectgroup theoryen_US
dc.subjectanalytical solutionen_US
dc.titleCompletely integrable relativistic Hamiltonian systems and separation of variables in Hermitian hyperbolic spacesen_US
dc.typeJournal Articleen_US
dc.identifier.doi10.1063/1.525943en_US
dc.relation.isPartOfJournal of Mathematical Physicsen_NZ
pubs.begin-page2022en_NZ
pubs.elements-id84075
pubs.end-page2034en_NZ
pubs.issue8en_NZ
pubs.volume24en_NZ


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