Higher Order Deformed Elliptic Ruijsenaars Operators
Journal article, 2022

We present four infinite families of mutually commuting difference operators which include the deformed elliptic Ruijsenaars operators. The trigonometric limit of this kind of operators was previously introduced by Feigin and Silantyev. They provide a quantum mechanical description of two kinds of relativistic quantum mechanical particles which can be identified with particles and anti-particles in an underlying quantum field theory. We give direct proofs of the commutativity of our operators and of some other fundamental properties such as kernel function identities. In particular, we give a rigorous proof of the quantum integrability of the deformed Ruijsenaars model.


Martin Hallnäs

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Edwin Langmann

Royal Institute of Technology (KTH)

Masatoshi Noumi

Royal Institute of Technology (KTH)

Hjalmar Rosengren

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Communications in Mathematical Physics

0010-3616 (ISSN) 1432-0916 (eISSN)

Vol. 392 2 659-689

Quasi-invariants of finite Coxeter groups and integrable systems

Swedish Research Council (VR) (2018-04291), 2019-01-01 -- 2022-12-31.

Combinatorics of elliptic lattice models

Swedish Research Council (VR) (2020-04221), 2021-01-01 -- 2024-12-31.

Subject Categories


Other Physics Topics

Mathematical Analysis



More information

Latest update

3/7/2024 9