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

• 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.

Subject headings

NATURVETENSKAP  -- Matematik -- Annan matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Other Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Keyword

quantization

Macdonald polynomials

Ruijsenaars–Schneider

Calogero–Moser–Sutherland

Calogero–Moser–Sutherland

Publication and Content Type

ref (subject category)

art (subject category)