Abstract
We consider finite and infinite-dimensional ghost-ridden dynamical systems whose Hamiltonians involve nonpositive definite kinetic terms. We point out the existence of three classes of such systems where the ghosts are benign, i.e., systems whose evolution is unlimited in time: (i) systems obtained from the variation of bounded-motion systems; (ii) systems describing motions over certain Lorentzian manifolds and (iii) higher-derivative models related to certain modified Korteweg-de Vries equations.
Highlights
A ghost-ridden dynamical quantum system is defined as a system whose spectrum is not bounded neither from below, nor from above
This is in particular the case for the quantum versions of the Ostrogradsky Hamiltonians [1], describing the dynamics of higher-derivative Lagrangians
Some particular examples of benign ghost-ridden Hamiltonians have been presented in previous works [8,11–15]
Summary
A ghost-ridden dynamical quantum system is defined as a system whose spectrum is not bounded neither from below, nor from above. Many ghost-ridden systems are sick: their evolution operator is not unitary Such systems involve classical trajectories that run into a singularity after a finite time of evolution (a blowup). There are, ghost-ridden systems with benign ghosts, in the sense that they do not exhibit a classical blowup and have a unitary quantum evolution operator. If α > 0, the point (1.6) lies within an “island of stability”—the trajectories with initial conditions sufficiently close to (1.6) do not go astray but exhibit an oscillatory behavior Some particular examples of benign ghost-ridden (nonlinearly interacting) Hamiltonians have been presented in previous works [8,11–15].
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