To the top

Page Manager: Webmaster
Last update: 9/11/2012 3:13 PM

Tell a friend about this page
Print version

Quantization and explicit… - University of Gothenburg, Sweden Till startsida
To content Read more about how we use cookies on

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

Journal article
Authors Tamas Görbe
Martin Hallnäs
Published in Journal of Integrable Systems
Volume 3
Issue 1
Publication year 2018
Published at Department of Mathematical Sciences
Language en
Keywords quantization, Macdonald polynomials, Ruijsenaars–Schneider, Calogero–Moser–Sutherland
Subject categories Mathematical Analysis, Other Mathematics


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.

Page Manager: Webmaster|Last update: 9/11/2012

The University of Gothenburg uses cookies to provide you with the best possible user experience. By continuing on this website, you approve of our use of cookies.  What are cookies?