Gauge invariant source terms in QCD
  We discuss how to implement the source terms in Quantum Chromodynamics (QCD) respecting gauge invariance and noncommutativity of color charge density operators. We start with decomposing the generating functional of QCD into constituents projected to have specified color charge density. We demonstrate that such a projection leads to the gauge invariant source terms consisting of a naive form accompanied by the density of states which cancels the gauge dependence. We then illustrate that this form is equivalently rewritten into a manifestly gauge invariant expression in terms of the Wilson line. We confirm that noncommutativity of color charge density operators is fulfilled in both representations of the source terms. We point out that our results are useful particularly to consider the problems of the quantum evolution in high energy QCD. 
Kenji Fukushima