Stable Self-Interacting Pais-Uhlenbeck Oscillator

Abstract

It is shown that the interacting Pais-Uhlenbeck oscillator necessarily leads to a description with a Hamiltonian that contains positive and negative energies associated with two oscillators. Descriptions with a positive definite Hamiltonians, considered by some authors, can hold only for a free Pais-Uhlenbeck oscillator. We demonstrate that the solutions of a self-interacting Pais-Uhlenbeck oscillator are stable on islands in the parameter space, as already observed in the literature. If we slightly modify the system, by considering a sine interaction term, and/or by taking unequal masses of the two oscillators, then the system is stable on the continents that extend from zero to infinity in the parameter space. Therefore, the Pais-Uhlenbeck oscillator is quite acceptable physical system.

14 pages, 5 figures, references added, typos corrected

References in corpus (9)

• Avoiding Dark Energy with 1/R Modifications of Gravity
• No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
• Solution to the ghost problem in fourth order derivative theories
• Supersymmetry vs ghosts
• Some Comments on Ghosts and Unitarity: The Pais-Uhlenbeck Oscillator Revisited
• Remarks on quantization of Pais-Uhlenbeck oscillators
• Astrophysical Evidence for the Non-Hermitian but $PT$-symmetric Hamiltonian of Conformal Gravity
• Quantum Field Theories in Spaces with Neutral Signatures
• On the unitarity of higher-dervative and nonlocal theories

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