# Ghosts in theories of gravity and holographic theories

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?

• 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) Jul 23 '14 at 15:51
• 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. Sep 3 '18 at 23:07
• 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. Sep 3 '18 at 23:08

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.