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| Format: | Preprint |
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2025
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| Online-Zugang: | https://arxiv.org/abs/2505.07869 |
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| _version_ | 1866918527076663296 |
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| author | Felski, Alexander Fring, Andreas Turner, Bethan |
| author_facet | Felski, Alexander Fring, Andreas Turner, Bethan |
| contents | We investigate the Pais-Uhlenbeck (PU) model, a paradigmatic example of a higher time-derivative theory, by identifying the Lie symmetries of its associated fourth-order dynamical equation. Exploiting these symmetries in conjunction with the model's Bi-Hamiltonian structure, we construct distinct Poisson bracket formulations that preserve the system's dynamics. Amongst other possibilities, this allow us to recast the PU model in a positive definite manner, offering a solution to the long-standing problem of ghost instabilities. Furthermore, we systematically explore a family of transformations that reduce the PU model to equivalent first-order, higher-dimensional systems. Finally we examine the impact on those transformations by adding interaction terms of potential form to the PU model and demonstrate how they usually break the Bi-Hamiltonian structure. Our approach yields a unified framework for interpreting and stabilising higher time-derivative dynamics through a symmetry analysis in some parameter regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_07869 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lie symmetries and ghost-free representations of the Pais-Uhlenbeck model Felski, Alexander Fring, Andreas Turner, Bethan Mathematical Physics Quantum Physics We investigate the Pais-Uhlenbeck (PU) model, a paradigmatic example of a higher time-derivative theory, by identifying the Lie symmetries of its associated fourth-order dynamical equation. Exploiting these symmetries in conjunction with the model's Bi-Hamiltonian structure, we construct distinct Poisson bracket formulations that preserve the system's dynamics. Amongst other possibilities, this allow us to recast the PU model in a positive definite manner, offering a solution to the long-standing problem of ghost instabilities. Furthermore, we systematically explore a family of transformations that reduce the PU model to equivalent first-order, higher-dimensional systems. Finally we examine the impact on those transformations by adding interaction terms of potential form to the PU model and demonstrate how they usually break the Bi-Hamiltonian structure. Our approach yields a unified framework for interpreting and stabilising higher time-derivative dynamics through a symmetry analysis in some parameter regime. |
| title | Lie symmetries and ghost-free representations of the Pais-Uhlenbeck model |
| topic | Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2505.07869 |