Three-dimensional ghost-free representations of the Pais-Uhlenbeck model from Tri-Hamiltonians
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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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 |