Completeness of superintegrability in two-dimensional constant-curvature spaces

E. G. Kalnins, J. M. Kress, G. S. Pogosyan, W. Miller

Research output: Contribution to journalArticlepeer-review

131 Scopus citations

Abstract

We classify the Hamiltonians H = p2x + p2y + V(x,y) of all classical superintegrable systems in two-dimensional complex Euclidean space with two additional second-order constants of the motion. We similarly classify the superintegrable Hamiltonians H = J21 + J22 + J23 + V(x, y, z) on the complex two-sphere where x2 + y2 + z2 = 1. This is achieved in all generality using properties of the complex Euclidean group and the complex orthogonal group.

Original languageEnglish (US)
Pages (from-to)4705-4720
Number of pages16
JournalJournal of Physics A: Mathematical and General
Volume34
Issue number22
DOIs
StatePublished - Jun 8 2001

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