Can we make sense out of negative kinetic energy?

Abstract: Many Quantum Field Theory models, either designed to improve the ultraviolet behavior via higher derivative terms or aimed at providing unified descriptions of Gravity, inevitably introduce negative-energy 'ghosts' states. These states raise fundamental questions regarding the stability of the theory. In this study, we investigate the time evolution of simplified quantum mechanical models consisting of two coupled normal and ghost subsystems. Although the full spectrum of these models is unbounded from below and, therefore, lacks a true ground state, we focus the time evolution of a 'would-be ground state': a zero-energy eigenstate of the decoupled system. By analyzing its metastability under interactions, we gain insights into the dynamics of ghost-like states. Contrary to the standard paradigm, our results demonstrate that, across a broad range of couplings, the would-be ground state does not decay and remains dynamically stable over long times. This provides evidence towards resolving the stability problems of Hamiltonians that are unbounded from below. We also discuss the connections with the corresponding classical and semiclassical dynamics.