Bi-Hamiltonian Structures and Equivalent Representations of the Pais-Uhlenbeck Model
Mathematical Physics
2025-10-01 v1 math.MP
Abstract
We provide a complete classification of all the ways the Pais-Uhlenbeck osicllator might be embedded in two dimensional space. We discuss the Bi-Hamiltonian structures of this model, and examine how alternative Hamiltonian structures might be generated from the dynamical Lie symmetries of the theory. We then examine how the Bi-Hamiltonian strucutre may be exploited to evade the problem of unbounded Hamiltonians that is usually associated with Higher Time Derivative Theories. The effect of interactions on this Bi-Hamiltonian structure is also considered.
Keywords
Cite
@article{arxiv.2509.26477,
title = {Bi-Hamiltonian Structures and Equivalent Representations of the Pais-Uhlenbeck Model},
author = {Bethan Turner},
journal= {arXiv preprint arXiv:2509.26477},
year = {2025}
}