Ghosts without Runaway Instabilities

We present a simple class of mechanical models where a canonical degree of freedom interacts with another one with a negative kinetic term, i.e., with a ghost. We prove analytically that the classical motion of the system is completely stable for all initial conditions, notwithstanding that the conserved Hamiltonian is unbounded from below and above. This is fully supported by numerical computations. Systems with negative kinetic terms often appear in modern cosmology, quantum gravity, and high energy physics and are usually deemed as unstable. Our result demonstrates that for mechanical systems this common lore can be too naive and that living with ghosts can be stable.

Automated summary

In this study, we introduce a class of mechanical models with a canonical degree of freedom interacting with a ghost. Analytically, we prove that the classical motion of the system is completely stable for all initial conditions, contradicting the common belief that systems with negative kinetic terms are unstable.