Quantization and explicit diagonalization of new compactified trigonometric Ruijsenaars–Schneider systems
Artikel i vetenskaplig tidskrift, 2018

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.

quantization

Macdonald polynomials

Ruijsenaars–Schneider

Calogero–Moser–Sutherland

Författare

Tamás Görbe

University of Szeged

Martin Hallnäs

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Journal of Integrable Systems

2058-5985 (eISSN)

Vol. 3 1 1-29

Ämneskategorier

Annan matematik

Matematisk analys

DOI

10.1093/integr/xyy015

Mer information

Senast uppdaterat

2018-08-06