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

• URL: http://arxiv.org/abs/2505.07869v1
• Date: Fri, 09 May 2025 15:16:40 GMT
• Title: Lie symmetries and ghost-free representations of the Pais-Uhlenbeck model
• Authors: Alexander Felski, Andreas Fring, Bethan Turner,
• Abstract summary: We investigate the Pais-Uhlenbeck (PU) model, a paradigmatic example of a higher time-derivative theory.<n>Exploiting Lie symmetries in conjunction with the model's Bi-Hamiltonian structure, we construct distinct Poisson bracket formulations.<n>Our approach yields a unified framework for interpreting and stabilising higher time-derivative dynamics.
• Score: 44.99833362998488
• License: http://creativecommons.org/licenses/by/4.0/
• 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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