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arXiv · 2505.07869

Lie symmetries and ghost-free representations of the Pais-Uhlenbeck model

Alexander Felski·Andreas Fring·Bethan Turner
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Abstract

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.

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Alexander Felski, Andreas Fring, Bethan Turner. 2025-05-09. Lie symmetries and ghost-free representations of the Pais-Uhlenbeck model. https://doi.org/10.1142/s0217732326500197

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