Is Feynman gauge reduce always physical gauge?

I heard in QCD, Feynman gauge does not always give correct physics.

The lecture says, "Feynman gauge gives physical gauge, if the theory contains only conserved current." Thus in QED Feynman gauge gives correct physics. (It is a physical gauge) But in QCD, If we neglect the ghost term in the Feynman rule, and compute its scattering amplitude via Feynman gauge, the answer may wrong.

(But also Lecture says, if we include the ghost term in the gluon loop, and apply Feynmann rule then it gives the correct answer. )

I always think in QCD and non-abelian gauge theory contains ghost term (due to its path integral measure). Thus I am confused about computing loop integrals without ghost term. If you know the intention of lecture, please give me some detail explanation.

Comments or example of computing QCD loops without ghost term which gives physical meaning are also welcome.

  • $\begingroup$ From what you say yourself, in a non-abelian gauge theory like QCD one should include diagrams with ghosts to get the correct amplitude, and if you ignore them you will generically get a wrong answer. I don't understand your question... $\endgroup$
    – J-T
    Dec 17, 2015 at 13:28
  • $\begingroup$ This was based on my lecturer, which i also get astonished. The formal expression of amplitude $J Green J$, and he addressed $J$ is conserved quantity, and thus it gives correct term. $\endgroup$
    – phy_math
    Dec 17, 2015 at 15:31
  • $\begingroup$ It might be related with Unitary gauge which removed the goldstones and ghost term in the theory $\endgroup$
    – phy_math
    Dec 18, 2015 at 1:36

1 Answer 1


There are indeed ghost-free gauges. An important example are the axial gauges,

$$n\cdot G_\mu^a=0,$$

where $G_\mu^a$ is the gluon field. They are much used for all the phenomenology involving the radiation by a quark or a gluon (one says a parton) of gluons nearly collinear to the parton momentum: Deep Inelastic Scattering (DIS), $pp$ collisions, $\gamma X$ and $\gamma\gamma$ collisions, ... for the partons in the initial state; production of hadrons or $\gamma$ for the partons in the final state. The reason is that in an axial gauge the dominant Feynman diagrams have a ladder structure with a strict ordering of the transverse momenta along the ladder, which makes computations very much easier. If you want to learn more, search for the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equation (DGLAP) which is a renormalisation group equation for the running of parton density function and fragmentation functions in the infrared domain: infrared because singularities appear when a gluon is radiated collinearly by a quark or another gluon.


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