City Research Online

Higher derivative Hamiltonians with benign ghosts from affine Toda lattices

Fring, A. ORCID: 0000-0002-7896-7161 & Turner, B. S. (2023). Higher derivative Hamiltonians with benign ghosts from affine Toda lattices. Journal of Physics A: Mathematical and Theoretical, 56(29), article number 295203. doi: 10.1088/1751-8121/ace0e6


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.

Publication Type: Article
Additional Information: This is an author-created, un-copyedited version of an article accepted for published in Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at
Subjects: Q Science > QA Mathematics
Departments: School of Science & Technology > Mathematics
[thumbnail of ClassTodaRev.pdf] Text - Accepted Version
This document is not freely accessible until 30 June 2024 due to copyright restrictions.

To request a copy, please use the button below.

Request a copy


Add to AnyAdd to TwitterAdd to FacebookAdd to LinkedinAdd to PinterestAdd to Email


Downloads per month over past year

View more statistics

Actions (login required)

Admin Login Admin Login