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Dynamical systems with benign ghosts
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Dynamical systems with benign ghosts
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We consider finite and infinite-dimensional ghost-ridden dynamical systems whose Hamiltonians involve non positive 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.
Forward citations
Cited by 3 Pith papers
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Ghost Degrees of Freedom Without Quantum Runaway: Exact Moment Bounds from an Operator Conservation Law
An exact operator conservation law from canonical commutation relations bounds second moments of a ghost-coupled oscillator for all time and states, preventing quantum runaway.
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Quantum mechanics with a ghost: Counterexamples to spectral denseness
Ghostly quantum systems can have discrete non-dense energy spectra under classical stability conditions, providing counterexamples to spectral denseness.
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Unitary Time Evolution and Vacuum for a Quantum Stable Ghost
A quantum ghost coupled polynomially to a harmonic oscillator has unitary evolution and a stable vacuum because a conserved quantity possesses a positive discrete spectrum.
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