Question

Is Feynman gauge reduce always physical gauge?

Answer 1

There are indeed ghost-free gauges. An important example are the axial gauges,
where 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), collisions, and collisions, ...

for the partons in the initial state; production of hadrons or 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.

Answer 2

The formal expression of amplitude JGreenJJGreenJ, and he addressed JJ is conserved quantity.