Quantization and explicit diagonalization of new compactified trigonometric RuijsenaarsSchneider systems
Abstract
Recently, Fehér and Kluck discovered, at the level of classical mechanics, new compactified trigonometric RuijsenaarsSchneider $n$particle systems, with phase space symplectomorphic to the $(n1)$dimensional complex projective space. In this article, we quantize the socalled 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 finitedimensional Hilbert space of complexvalued functions supported on a uniform lattice over the classical configuration space, and their joint eigenfunctions are constructed in terms of discretized $A_{n1}$ Macdonald polynomials with unitary parameters.
 Publication:

arXiv eprints
 Pub Date:
 July 2017
 arXiv:
 arXiv:1707.08483
 Bibcode:
 2017arXiv170708483G
 Keywords:

 Mathematical Physics;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 27 pages, 4 figures