Dynamical systems with benign ghosts

TL;DR

This paper explores specific classes of ghost-ridden dynamical systems with non-positive definite Hamiltonians, demonstrating conditions under which these systems exhibit benign, unlimited evolution in time.

Contribution

It identifies three classes of ghost systems where ghosts are benign, expanding understanding of their behavior in finite and infinite-dimensional contexts.

Findings

Benign ghosts allow unlimited evolution.

Three classes of systems with benign ghosts identified.

Connections to Lorentzian manifolds and higher-derivative models.

Abstract

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.