  We investigate the relationship between colour confinement and the gauge
independent Cho-Duan-Ge Abelian decomposition.
  The decomposition is defined in terms of a colour field $n$; the principle
novelty of our study is that we have defined this field in terms of the
eigenvectors of the Wilson Loop. This establishes an equivalence between the
path ordered integral of the non-Abelian gauge fields with an integral over an
Abelian restricted gauge field which is tractable both theoretically and
numerically in lattice QCD. We circumvent path ordering without needing an
additional path integral. By using Stokes' theorem, we can compute the Wilson
Loop in terms of a surface integral over a restricted field strength, and show
that the restricted field strength may be dominated by certain structures,
which occur when one of the quantities parametrising the colour field $n$ winds
itself around a non-analyticity in the colour field. If they exist, these
structures will lead to a area law scaling for the Wilson Loop and provide a
mechanism for quark confinement.
  We search for these structures in quenched lattice QCD. We perform the
Abelian decomposition, and compare the electric and magnetic fields with the
patterns expected theoretically. We find that the restricted field strength is
dominated by objects which may be peaks a single lattice spacing in size or
extended string-like lines of electromagnetic flux. The objects are not
isolated monopoles, as they generate electric fields in addition to magnetic
fields, and the fields are not spherically symmetric, but may be either caused
by a monopole/anti-monopole condensate, some other types of topological objects
or a combination of these. Removing these peaks removes the area law scaling of
the string tension, suggesting that they are responsible for confinement.

High Energy Physics - Lattice;High Energy Physics - Theory