  Boundary operators are gauge invariant operators whose form factors
correspond to boundary contributions of BCFW shifts. In gauge theory, the
boundary operators contain infinite series, which are constrained by gauge
symmetry. We compute the boundary operators of all possible BCFW shifts in
Yang-Mills theory and QCD, and show that the infinite series can be elegantly
organized into Wilson lines, which are natural building blocks for non-local
gauge invariant operators. We comment on their connection to jet functions and
gauge invariant off-shell amplitudes. We also verify our results by studying
various BCFW shifts of four and five-point amplitudes.
