Quantum 2025 – wissenschaftliches Programm

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TUE: Tuesday Contributed Sessions

TUE 10: Foundational / Mathematical Aspects – Rigorous Results

TUE 10.5: Vortrag

Dienstag, 9. September 2025, 15:15–15:30, ZHG103

Lie symmetries and ghost-free representations of the Pais-Uhlenbeck model — •Alexander Felski — Max Planck Institute for the Science of Light, Erlangen, Germany

Ghost-ridden quantum systems manifest in various forms. Typically, this means that parts of their spectra are not bounded from below or that they contain non-normalisable states, leading to a violation of unitarity. We investigate the Pais-Uhlenbeck model, a prominently ghost-ridden system and 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. This allows us to recast the Pais-Uhlenbeck 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 Pais-Uhlenbeck model to equivalent first-order, higher-dimensional systems. Our approach yields a unified framework for interpreting and stabilizing higher time-derivative dynamics through a symmetry analysis.

Keywords: Higher time-derivative theories; Bi-Hamiltonian systems; Pais-Uhlenbeck oscillator