Higher derivative Hamiltonians with benign ghosts from affine Toda lattices

TL;DR

This paper investigates affine Toda lattice theories with higher derivative Hamiltonians, providing evidence that certain integrable systems can have benign ghost sectors, and explores their classical phase space behaviors.

Contribution

It demonstrates that higher charge Hamiltonians in affine Toda lattices can exhibit benign ghost sectors, expanding understanding of higher derivative theories in integrable systems.

Findings

Some theories show oscillatory and benign divergent behaviors with ghosts.

No trajectories reached finite-time singularities.

High sensitivity to initial conditions in certain Lie algebra representations.

Abstract

We provide further evidence for Smilga's conjecture that higher charges of integrable systems are suitable candidates for higher derivative theories that possess benign ghost sectors in their parameter space. As concrete examples we study the properties of the classical phase spaces for a number of affine Toda lattices theories related to different types of Kac-Moody algebras. We identify several types of scenarios for theories with higher charge Hamiltonians: some that possess oscillatory, divergent, benign oscillatory and benign divergent behaviour when ghost sectors are present in the quantum theory. No divergent behaviour was observed for which the trajectories reach a singularity in finite time. For theories based on particular representations for the Lie algebraic roots we found an extreme sensitivity towards the initial conditions governed by the Poisson bracket relations between the centre-of-mass coordinate and the charges.