Bi-Hamiltonian Structures and Equivalent Representations of the Pais-Uhlenbeck Model

2025/09/30 by Turner, Bethan
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2509.26477

Abstract

We provide a complete classification of all the ways the Pais-Uhlenbeck osicllator might be embedded in two dimensional space. We discuss the Bi-Hamiltonian structures of this model, and examine how alternative Hamiltonian structures might be generated from the dynamical Lie symmetries of the theory. We then examine how the Bi-Hamiltonian strucutre may be exploited to evade the problem of unbounded Hamiltonians that is usually associated with Higher Time Derivative Theories. The effect of interactions on this Bi-Hamiltonian structure is also considered.

Citations

• Three-dimensional ghost-free representations of the Pais-Uhlenbeck model from Tri-Hamiltonians
• Lie symmetries and ghost-free representations of the Pais-Uhlenbeck model
• Foundations of Ghost Stability
• STABLE SELF-INTERACTING PAIS–UHLENBECK OSCILLATOR
• Hamiltonian structures for Pais-Uhlenbeck oscillator
• A new type of isotropic cosmological models without singularity
• Renormalization of higher-derivative quantum gravity

Related

• Lie symmetries and ghost-free representations of the Pais-Uhlenbeck model
• New (Ghost-Free) Formulation of the Pais-Uhlenbeck Oscillator
• Hamiltonian structures for Pais-Uhlenbeck oscillator
• Three-dimensional ghost-free representations of the Pais-Uhlenbeck model from Tri-Hamiltonians
• Bi-Hamiltonian structure as a shadow of non-Noether symmetry