Clebsch-Gordan problem for three-dimensional Lorentz group in the elliptic basis: I. Tensor product of continuous series

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dc.contributor.authorKerimov, GA
dc.contributor.authorVerdiyev, YA
dc.date.accessioned2024-06-12T11:20:45Z
dc.date.available2024-06-12T11:20:45Z
dc.date.issued1998
dc.departmentTrakya Üniversitesien_US
dc.description.abstractThis paper is the first of two papers devoted to the study of the Clebsch-Gordan (CG) problem for the three-dimensional Lorentz group SO0(2, 1) in an elliptic (or SO(2)) basis. Here we describe the reduction of the tensor product of two unitary irreducible representations (UIRs) of the continuous series, i.e. belonging tb either the principal or complementary series. The corresponding CG coefficients ate defined as matrix elements of an intertwining operator between the tensor product representation and the irreducible component appearing in the decomposition; We then obtain an expression for CG coefficients in terms of a single function, namely in terms of the bilateral series H-3(3)(1) with unit argument defined in the complex space C-3 of the variable j(1), j(2), j. In the general case the H-3(3)(1) functions are expressed in terms of two hypergeometric functions F-3(2) with unit argument; however, it reduces to the single F-3(2)(1) function if at least one of the coupling UIRs belong to a discrete series. We derive a completeness relation for CG coefficients for all the cases under consideration.en_US
dc.identifier.doi10.1088/0305-4470/31/15/020
dc.identifier.endpage3593en_US
dc.identifier.issn0305-4470
dc.identifier.issue15en_US
dc.identifier.scopus2-s2.0-0032540082en_US
dc.identifier.scopusqualityN/Aen_US
dc.identifier.startpage3573en_US
dc.identifier.urihttps://doi.org/10.1088/0305-4470/31/15/020
dc.identifier.urihttps://hdl.handle.net/20.500.14551/25762
dc.identifier.volume31en_US
dc.identifier.wosWOS:000073436200020en_US
dc.identifier.wosqualityQ2en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherIop Publishing Ltden_US
dc.relation.ispartofJournal Of Physics A-Mathematical And Generalen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subject[No Keywords]en_US
dc.titleClebsch-Gordan problem for three-dimensional Lorentz group in the elliptic basis: I. Tensor product of continuous seriesen_US
dc.typeArticleen_US

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