Quantization and explicit diagonalization of new compactified trigonometric Ruijsenaars–Schneider systems

Görbe, TamasUniversity of Szeged,University of Szeged / Szegedi Tudományegyetem (författare)

Recently, Fehér and Kluck discovered, at the level of classical mechanics, new compactified trigonometric Ruijsenaars–Schneider n -particle systems, with phase space symplectomorphic to the (n−1) -dimensional complex projective space. In this article, we quantize the so-called type (i) instances of these systems and explicitly solve the joint eigenvalue problem for the corresponding quantum Hamiltonians by generalising previous results of van Diejen and Vinet. Specifically, the quantum Hamiltonians are realized as discrete difference operators acting in a finite-dimensional Hilbert space of complex-valued functions supported on a uniform lattice over the classical configuration space, and their joint eigenfunctions are constructed in terms of discretized An−1 Macdonald polynomials with unitary parameters.

Hallnäs, Martin,1979Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,Chalmers tekniska högskola,Chalmers University of Technology,University of Gothenburg(Swepub:cth)hallnas (författare)
University of SzegedInstitutionen för matematiska vetenskaper (creator_code:org_t)

Ingår i:Journal of Integrable Systems: Oxford University Press (OUP)3:12058-5985

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