Diagonalization of the infinite q-boson system

TL;DR

This paper introduces a hierarchy of commuting operators for the infinite q-boson system, diagonalizes them using Hall-Littlewood functions, and computes the n-particle scattering operator, advancing understanding of integrable quantum systems.

Contribution

It presents a new hierarchy of commuting operators for the q-boson system and demonstrates their simultaneous diagonalization with Hall-Littlewood functions, providing explicit scattering operator calculations.

Findings

Hierarchy of commuting operators constructed and diagonalized.

Hall-Littlewood functions serve as simultaneous eigenfunctions.

Explicit computation of the n-particle scattering operator.

Abstract

We present a hierarchy of commuting operators in Fock space containing the q-boson Hamiltonian on $\mathbb{Z}$ and show that the operators in question are simultaneously diagonalized by Hall-Littlewood functions. As an application, the n-particle scattering operator is computed.