# Dynamical systems with benign ghosts

@inproceedings{Damour2021DynamicalSW, title={Dynamical systems with benign ghosts}, author={T. Damour and Andrei V. Smilga}, year={2021} }

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…

## One Citation

Gauging the superconformal group with a graded dual operator

- Physics
- 2021

Based on the superconformal algebra we construct a dual operator that introduces a grading among bosonic generators independent of the boson/fermion grading of the superalgebra. This dual operator…

## References

SHOWING 1-10 OF 34 REFERENCES

Classical and Quantum Dynamics of Higher-Derivative Systems

- Physics
- 2017

A brief review of the physics of systems including higher derivatives in the Lagrangian is given. All such systems involve ghosts, i.e. the spectrum of the Hamiltonian is not bounded from below and…

Supersymmetry vs ghosts

- Physics, Mathematics
- 2006

We consider the simplest nontrivial supersymmetric quantum mechanical system involving higher derivatives. We unravel the existence of additional bosonic and fermionic integrals of motion forming a…

Some Comments on Ghosts and Unitarity: The Pais-Uhlenbeck Oscillator Revisited

- Physics
- 2013

We give a simple discussion of ghosts, unitarity violation, negative norm states and quantum vs classical behavior in the simplest model with four derivative action - the Pais-Uhlenbeck oscillator.…

The global Cauchy problem for the non linear Klein-Gordon equation-II

- Mathematics
- 1986

Abstract We study the Cauchy problem for a class of non linear Klein-Gordon equations of the type φ .. − Δ φ + f ( φ ) = 0 by a contraction method. We prove the existence and uniqueness of strongly…

Global solutions of the Einstein-Maxwell equations in higher dimensions

- Physics
- 2006

We consider the Einstein–Maxwell equations in space-dimension n. We point out that the Lindblad–Rodnianski stability proof applies to those equations whatever the space-dimension n ≥ 3. In even…

Supersymmetric field theory with benign ghosts

- Physics
- 2014

We construct a supersymmetric (1+1)-dimensional field theory involving extra derivatives and associated ghosts: the spectrum of the Hamiltonian is not bounded from below or from above. In spite of…

Comment on "Dirac Quantization of Pais-Uhlenbeck Fourth Order Oscillator"

- Mathematics, Physics
- 2007

The structure of Pais-Uhlenbeck oscillator in the equal-frequency limit has been recently studied by Mannheim and Davidson [Phys.Rev. A71 (2005), 042110]. It appears that taking this limit , as…

Comments on the Dynamics of the Pais-Uhlenbeck Oscillator ?

- Physics, Mathematics
- 2009

We discuss the quantum dynamics of the Pais-Uhlenbeck oscillator. The Lagrangian of this higher-derivative model depends on two frequencies. When the frequencies are different, the free PU oscillator…

The global stability of Minkowski space-time in harmonic gauge

- Physics, Mathematics
- 2004

We give a new proof of the global stability of Minkowski space originally established in the vacuum case by Christodoulou and Klainerman. The new approach, which relies on the classical harmonic…