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I want to understand when a theory leads to ghosts in gravity. Is there any relation between ghosts and non-linear higher order theories? Ghost is a clasical or quantum field concept?

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  • $\begingroup$ Do you know Faddeev-Popov gauge fixing and BRST symmetry for ordinary gauge theories? If not, you should start there to understand how and why ghosts arise. (Ghosts are a QFT concept) $\endgroup$
    – ACuriousMind
    Jul 23 '14 at 15:51
  • $\begingroup$ I suspect that they arise from the quantisation of gauge theories with non-abelian gauge group like SU(2) or SU(3); mainly because I don't recall ghosts being a phenomena of electrodynamics which is an abelian gauge theory ie U(1) is abelian. $\endgroup$ Sep 3 '18 at 23:07
  • $\begingroup$ I don't recall ghosts being a phenomenon in the two main theories of quantum gravity - either string theory or LQG - I could be wrong though. $\endgroup$ Sep 3 '18 at 23:08
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Ghosts also arise in the context of the classic theory through Ostrogradsky theorem. You should take a look at this paper:

Woodard, Richard. “Ostrogradskys Theorem on Hamiltonian Instability.” Scholarpedia, vol. 10, no. 8, 2015, p. 32243., doi:10.4249/scholarpedia.32243.

It's available on arXiv.

The general ideia is that, given a non-degenerate Lagrangian of the form $$\mathcal{L}=\mathcal{L}(x,\dot x, \ddot x, ...)\;,$$ the associated Hamiltonian is necessarily linear in almost all of the canonical momenta, and the Hamiltonian is unbounded bellow, rendering the system unstable. It implies that non-degenerate systems with higher than one time-derivative dependence suffer from ghost-like (unphysical) degrees of freedom.

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