On the Quantization of a Self-Dual Integrable System

TL;DR

This paper applies canonical quantization to a self-dual particle system linked to the KP hierarchy, explicitly deriving the quantum Hamiltonian and wave function, confirming bispectrality as predicted by physics hypotheses.

Contribution

It explicitly determines the quantum Hamiltonian and wave function for a self-dual integrable system, confirming bispectrality in this context.

Findings

Quantum Hamiltonian explicitly derived

Wave function shown to be symmetric (bispectral)

Supports hypothesis of bispectrality in quantum integrable systems

Abstract

In this note, we apply canonical quantization to the self-dual particle system describing the motion of poles to a higher rank solution of the KP hierarchy, explicitly determining both the quantum Hamiltonian and the wave function. It is verified that the quantum Hamiltonian is trivially bispectral (that is, that the wave function can be taken to be symmetric) as predicted by a widely held hypothesis of mathematical physics.