Living with ghosts: stable edition

ABSTRACT: I will discuss our recent works Phys.Rev.Lett. 128 (2022) 4, 041301 and ePrint: 2305.09631. There we presented a large class of mechanical models where a canonical degree of freedom interacts with another one with a negative kinetic term, i.e., with a ghost and yet the system is totally stable.

We proved analytically that the classical motion of the system is finite i.e. Lagrange stable for all initial conditions, notwithstanding that the conserved Hamiltonian is unbounded from below and above. Moreover, there are Lyapunov stable equilibrium configurations. Numerical computations fully supported this.

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 naïve and that a stable living with ghosts is possible.