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dc.contributor.authorKalnins, Ernie G.en_NZ
dc.contributor.authorMiller, W., Jr.en_NZ
dc.contributor.authorSubag, Eyalen_NZ
dc.date.accessioned2016-05-31T02:03:54Z
dc.date.available2016en_NZ
dc.date.available2016-05-31T02:03:54Z
dc.date.issued2016en_NZ
dc.identifier.citationKalnins, E. G., Miller, W., Jr., & Subag, E. (2016). Bôcher contractions of conformally superintegrable Laplace equations. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 12. http://doi.org/10.3842/SIGMA.2016.038en
dc.identifier.urihttps://hdl.handle.net/10289/10286
dc.description.abstractThe explicit solvability of quantum superintegrable systems is due to symmetry, but the symmetry is often “hidden”. The symmetry generators of 2nd order superintegrable systems in 2 dimensions close under commutation to define quadratic algebras, a generalization of Lie algebras. Distinct systems on constant curvature spaces are related by geometric limits, induced by generalized Inönü–Wigner Lie algebra contractions of the symmetry algebras of the underlying spaces. These have physical/geometric implications, such as the Askey scheme for hypergeometric orthogonal polynomials. However, the limits have no satisfactory Lie algebra contraction interpretations for underlying spaces with 1- or 0-dimensional Lie algebras. We show that these systems can be best understood by transforming them to Laplace conformally superintegrable systems, with flat space conformal symmetry group SO(4, ℂ), and using ideas introduced in the 1894 thesis of Bôcher to study separable solutions of the wave equation in terms of roots of quadratic forms. We show that Bôcher’s prescription for coalescing roots of these forms induces contractions of the conformal algebra so(4, ℂ) to itself and yields a mechanism for classifying all Helmholtz superintegrable systems and their limits. In the paperActa Polytechnica, to appear, arXiv:1510.09067], we announced our main findings. This paper provides the proofs and more details.en_NZ
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.rightsThis article is published under the terms of the Creative Commons Attribution-ShareAlike License .
dc.titleBôcher contractions of conformally superintegrable Laplace equationsen_NZ
dc.typeJournal Article
dc.identifier.doi10.3842/SIGMA.2016.038en_NZ
dc.relation.isPartOfSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)en_NZ
pubs.elements-id138749
pubs.volume12en_NZ
dc.identifier.eissn1815-0659en_NZ
uow.identifier.article-no038


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