City Research Online

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 allows us to recast the PU model in a positive definite manner, adding another 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 stabilizing higher time-derivative dynamics through a symmetry analysis in some parameter regime.

Publication Type:	Article
Additional Information:	Electronic version of an article published as Felski, A., Fring, A. & Turner, B. (2026). Lie symmetries and Ghost-free representations of the Pais–Uhlenbeck model. Modern Physics Letters A, article number 2650019. doi: 10.1142/s0217732326500197 © copyright World Scientific Publishing Company https://www.worldscientific.com/
Publisher Keywords:	Higher time-derivative theories, Lie symmetries, Bi-Hamiltonian systems
Subjects:	Q Science > QC Physics
Departments:	School of Science & Technology School of Science & Technology > Department of Mathematics
SWORD Depositor:	Symplectic Administrator

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