Plane waves, integrable quantum systems, Green functions and the groups SO(p,q), p<=q

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dc.contributor.authorVerdiyev, YA
dc.date.accessioned2024-06-12T11:20:44Z
dc.date.available2024-06-12T11:20:44Z
dc.date.issued1997
dc.departmentTrakya Üniversitesien_US
dc.description.abstractPlane waves on symmetric spaces (SS) X = SO(p,q)/SO(p) circle times SO(q) of rank p, p less than or equal to q, are constructed by realization of the irreducible representations (principal series) of the group SO(p,q) in the space of infinitely differentiable homogeneous vector functions F(y(i)) on cones [y(i), y(i)] = 0,y(i) epsilon Y-i, with values in the representation space of the stability subgroups SO(p - i, q - i), i = 1,..., p. We define the cones Y-i = Lim X(alpha(i),...,alpha(p)), alpha(i) --> infinity, corresponding to the SS X related with Cartan involutive automorphism sigma(g) = Igl, g epsilon SO(p,q), where I = diag(1,...,1,-1,...,-1) is the metric tensor of the pseudo-Euclidean space R-p.4 Calculating Harish-Chandra c-functions the orthogonality, completeness conditions and addition theorems for plane waves are derived. The integrable n-body quantum systems related to groups SO(p, q) are considered. The explicit expressions for the Green functions in the case SS X of rank p = 1 and the integral representation in the general case are given.en_US
dc.identifier.doi10.1088/0305-4470/30/11/033
dc.identifier.endpage4107en_US
dc.identifier.issn0305-4470
dc.identifier.issue11en_US
dc.identifier.scopus2-s2.0-0038867291en_US
dc.identifier.scopusqualityN/Aen_US
dc.identifier.startpage4089en_US
dc.identifier.urihttps://doi.org/10.1088/0305-4470/30/11/033
dc.identifier.urihttps://hdl.handle.net/20.500.14551/25760
dc.identifier.volume30en_US
dc.identifier.wosWOS:A1997XE20800033en_US
dc.identifier.wosqualityQ1en_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.titlePlane waves, integrable quantum systems, Green functions and the groups SO(p,q), p<=qen_US
dc.typeArticleen_US

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