Integrable scattering theory with higher derivative Hamiltonians

TL;DR

This paper extends scattering theory to systems with higher derivative Hamiltonians, using integrable Calogero models to compute classical phase shifts and discussing quantum implications.

Contribution

It introduces a generalization of scattering theory for higher derivative Hamiltonian systems based on integrable Calogero models.

Findings

Classical phase shifts computed for higher derivative Hamiltonian systems.

Discussion on quantum versions of these higher derivative integrable systems.

Extension of standard scattering theory to new classes of Hamiltonians.

Abstract

We discuss how a standard scattering theory a of multi-particle theory generalises to systems based on Hamiltonians that involve higher-order derivatives in their quantum mechanical formulation. As concrete examples, we consider Hamiltonian systems built from higher-order charges of Calogero and Calogero-Moser systems. Exploiting the integrability of these systems, we compute the classical phase shifts and briefly comment on the quantum versions of these types of theories.