  I clarify, restate and show more clearly some key points I raised in a number
of papers that discussed the non-linear gauge-fixing condition and quark
confinement. I also correct some errors, which do not detract from the key
findings, found in the original papers. However, there are two major
corrections I will make in this paper, the first is on the proof of the
Parisi-Sourlas mechanism and the second is on the effective action for the
'gluons', which leads to a direct proof of gluons being confined inside
hadrons. The correction also leads to how the mass gap will be calculated,
which was explicitly done in 2D.
  The starting point is that contrary to the prevailing ideas in the
literature, the Coulomb gauge is an incomplete gauge-fixing condition in the
sense that there are field configurations that cannot be gauge transformed to
the Coulomb gauge. In other words the orbit of these configurations will not
intersect the Coulomb gauge surface. I proposed the non-linear gauge condition
precisely because it includes the Coulomb gauge in the high energy (short
distance) regime and the quadratic regime (the large distance regime where the
running coupling becomes large), where the gauge fields cannot be gauge
transformed to the Coulomb surface. We proposed a new decomposition of the
gauge potential in the non-linear regime, which involves an isoscalar (the
divergence of the gauge field) and a new vector field, which exhibits a mass
gap and confinement. When we add the quarks, we find that they are localized to
a given distance scale and has an effective four-Fermi action with a linear
potential. Thus, we have shown a mass gap for gluons and confinement for both
dynamical quarks and gluons.
