Faddeev-Popov ghost

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In physics, Faddeev-Popov ghosts are auxiliary fields which appear in quantum field theories involving redundancies of description, such as gauge theories. In the path integral formulation of quantum field theory, the path integrals should not overcount field configurations related by gauge symmetries since those correspond to the same physical state. Consequently, the measure of the path integrals contains an additional factor, which does not allow obtaining various results directly from the action using the regular methods (e.g., Feynman diagrams). It is possible, however, to modify the action such that the regular methods will be applicable. This often requires adding some additional fields, which are called the ghost fields. This technique is called the Faddeev-Popov procedure (see also BRST quantization). The ghost fields are a computational tool, and they do not correspond to any real particles.

The Faddeev-Popov ghosts violate the spin-statistics relation. For example, in the non-abelian gauge theories of the standard model the ghosts are scalar fields (spin 0), but they anticommute (like fermions). In general, anticommuting ghosts are associated with bosonic symmetries, while commuting ghosts are associated with fermionic symmetries.

The Faddeev-Popov ghosts are sometimes referred to as "good ghosts". The "bad ghosts" represent another, more general meaning of the word "ghost" in theoretical physics: states of negative norm - or fields with the wrong sign of the kinetic term - whose existence allows the probabilities to be negative.Template:Quantum-stub