Talk:Faddeev–Popov ghost

Gauge theories
The article states:
 * In physics, Faddeev-Popov ghosts are auxiliary fields which appear in quantum field theories involving redundancies of description, such as gauge theories.

But are there any other situations in which ghost particles are used, apart from gauge theories, as implied by this wording?


 * OK, I fixed it. Yevgeny Kats 10:53, 23 August 2006 (UTC)

"Not real" does not mean "virtual" in the context of ghosts
I see my clarification of what is meant by saying ghost partcles are not real:
 * The ghost fields/particles are a computational tool, appearing as internal particles but not in external states, since the gauge is normally fixed by the boundary conditions. In this sense they do not correspond to other real or virtual particles.

has been reverted back to


 * The ghost fields are a computational tool, and they do not correspond to any real particles.

with the comment "rv MichaelCPrice: not real -does- mean virtual".

This is incorrect, unless the sentence was meant to read:


 * The ghost fields are a computational tool, and they correspond to virtual particles.

which I rather doubt.

--Michael C. Price talk 11:00, 23 August 2006 (UTC)


 * The ghost fields may appear as virtual particles, and they may not appear as real particles (while usual fields, such as photons, can appear in both forms). Yevgeny Kats 11:48, 23 August 2006 (UTC)
 * Then let's say they only appear as virtual particles, if that's what you mean. --Michael C. Price talk 12:35, 23 August 2006 (UTC)

Good and bad ghosts - is there a difference?
The article says:
 * 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.

But don't all ghosts imply negative norm states? Faddeev-Popov ghost propagators always have the opposite sign from the analogous non-ghost propagators, which implies the opposite sign for their norm -- doesn't it? --Michael C. Price talk 12:48, 2 July 2007 (UTC)

Eduardo Fradkin's "Quantum Field Theory: An Integrated Approach", chapter 9 section 8 explains that the Faddeev-Popov ghost fields cannot actually create any physical states, since the Faddeev-Popov ghost fields are fermionic operators that are not spinors (they have integer spin). So they don't allow probabilities to be negative. At least as far as I understand. — Preceding unsigned comment added by 183.83.130.196 (talk) 10:15, 25 December 2021 (UTC)

Appearance in Feynman diagrams - request diagram
The article says: "In Feynman diagrams the ghosts appear as closed loops wholly composed of 3-vertices, attached to the rest of the diagram via a gauge particle at each 3-vertex." Can someone add an example of such a diagram? RJFJR (talk) 22:05, 27 February 2014 (UTC)

Faddeev-Popov ghosts outside of perturbation theory
There is no need to introduce Faddeev-Popov ghosts outside of perturbation theory. In non-pertubative lattice gauge field calculations, ghosts are not required.

Since physical observable are gauge independent the reasoning in: "The necessity for Faddeev–Popov ghosts follows from the requirement that in the path integral formulation, quantum field theories should yield unambiguous, non-singular solutions. This is not possible when a gauge symmetry is present since there is no procedure for selecting any one solution from a range of physically equivalent solutions, all related by a gauge transformation." make no sense to me. One way to look at the need for Faddeev-Popov ghosts in perturbation theory is the zero modes in the propagators. I suggest to revise the section (header) "Overcounting in Feynman path integrals".

--Achimwu (talk) 00:05, 1 September 2015 (UTC)