Joint eigenfunctions for the relativistic Calogero-Moser Hamiltonians of hyperbolic type. I. First steps

TL;DR

This paper introduces a recursion scheme to construct joint eigenfunctions for hyperbolic relativistic Calogero-Moser Hamiltonians, advancing the understanding of integrable N-particle systems through kernel identities and analytic methods.

Contribution

It develops a novel recursion scheme based on kernel identities to explicitly construct joint eigenfunctions for hyperbolic relativistic Calogero-Moser systems, including free cases.

Findings

Scheme is viable for arbitrary N in free cases

Provides analytic tools for eigenfunction properties

Lays groundwork for future full solutions

Abstract

We present and develop a recursion scheme to construct joint eigenfunctions for the commuting analytic difference operators associated with the integrable N-particle systems of hyperbolic relativistic Calogero-Moser type. The scheme is based on kernel identities we obtained in previous work. In this first paper of a series we present the formal features of the scheme, show explicitly its arbitrary-N viability for the `free' cases, and supply the analytic tools to prove the joint eigenfunction properties in suitable holomorphy domains.