Higher Order Deformed Elliptic Ruijsenaars Operators

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.

Automated summary

The paper introduces four infinite families of mutually commuting difference operators, including the deformed elliptic Ruijsenaars operators. These operators provide a quantum mechanical description of two kinds of relativistic quantum mechanical particles, with direct proofs of the commutativity and other fundamental properties being given. The paper rigorously proves the quantum integrability of the deformed Ruijsenaars model.