Three-dimensional ghost-free representations of the Pais-Uhlenbeck model from Tri-Hamiltonians

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Hauptverfasser: Felski, Alexander, Fring, Andreas, Turner, Bethan
Format: Preprint
Veröffentlicht: 2025
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author Felski, Alexander
Fring, Andreas
Turner, Bethan
author_facet Felski, Alexander
Fring, Andreas
Turner, Bethan
contents We present a detailed analysis of the sixth-order Pais-Uhlenbeck oscillator and construct three-dimensional ghost-free representations through a Tri-Hamiltonian framework. We identify a six-dimensional Abelian Lie algebra of the PU model's dynamical flow and derive a hierarchy of conserved Hamiltonians governed by multiple compatible Poisson structures. These structures enable the realisation of a complete Tri-Hamiltonian formulation that generates identical dynamical flows. Positive-definite Hamiltonians are constructed, and their relation to the full Tri-Hamiltonian hierarchy is analysed. Furthermore, we develop a mapping between the PU model and a class of three-dimensional coupled second-order systems, revealing explicit conditions for ghost-free equivalence. We also explore the consequences of introducing interaction terms, showing that the multi-Hamiltonian structure is generally lost in such cases.
format Preprint
id arxiv_https___arxiv_org_abs_2509_13925
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Three-dimensional ghost-free representations of the Pais-Uhlenbeck model from Tri-Hamiltonians
Felski, Alexander
Fring, Andreas
Turner, Bethan
Mathematical Physics
Quantum Physics
We present a detailed analysis of the sixth-order Pais-Uhlenbeck oscillator and construct three-dimensional ghost-free representations through a Tri-Hamiltonian framework. We identify a six-dimensional Abelian Lie algebra of the PU model's dynamical flow and derive a hierarchy of conserved Hamiltonians governed by multiple compatible Poisson structures. These structures enable the realisation of a complete Tri-Hamiltonian formulation that generates identical dynamical flows. Positive-definite Hamiltonians are constructed, and their relation to the full Tri-Hamiltonian hierarchy is analysed. Furthermore, we develop a mapping between the PU model and a class of three-dimensional coupled second-order systems, revealing explicit conditions for ghost-free equivalence. We also explore the consequences of introducing interaction terms, showing that the multi-Hamiltonian structure is generally lost in such cases.
title Three-dimensional ghost-free representations of the Pais-Uhlenbeck model from Tri-Hamiltonians
topic Mathematical Physics
Quantum Physics
url https://arxiv.org/abs/2509.13925