STABLE SELF-INTERACTING PAIS–UHLENBECK OSCILLATOR

Abstract

It is shown that the interacting Pais–Uhlenbeck (PU) 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 PU oscillator. We demonstrate that the solutions of a self-interacting PU 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 PU oscillator is quite acceptable physical system.