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.

Figure 1

Total potential energy is plotted for coupling constant $\lambda =1/3$ in the interaction potential [Eq. (2)].

Figure 2

The plot of $x(t)$ and $y(t)$.

Figure 3

The projection of the trajectory onto the $xy$ plane. The color represents the value of $t$.

Figure 4

The projection of the trajectory onto the $y{p}_y$ plane. The color represents the value of $t$.