These Ghosts are introduced to maintain gauge invariance in theories where the local field components exceeds the number of physical degrees of freedom.
An example of the need of ghost fields is the photon, which is usually described by a four component vector potential Aμ, even if light has only two allowed polarizations in the vacuum.
Good ghosts are virtual particles, that are introduced to maintain mathematical consistencies in a gauge theory, and they often serve as a tool for regularization.
Faddeev–Popov ghosts are extraneous anticommuting fields which are introduced to maintain the consistency of the path integral formulation in non-abelian gauge theories, such as the ones describing strong force.
Here's how this works: Person A tries to describe the motion of X particle, but his description consists of too many unnecessary, unphysical variables —many of which don't correspond to anything real or observable.
We have a real scalar field φ with the following action where a and b are positive constants and The theories of ghost condensate predict specific non-Gaussianities of the cosmic microwave background.