  Up until now, the BCFW technique has been a widely used method in getting the
amplitudes in various theories. Usually, the vanishing of the boundary term is
necessary for the efficiency of the method. However, there are also many kinds
of amplitudes which will have boundary terms. Hence it will be nice if it is
possible to get the boundary terms in an efficient manner. As is well-known, in
gauge theory the Ward identity imposes constraints on the form of the
amplitude. In [1], we studied the Ward identity with a pair of shifted lines
and the implied recursion relations. In this article, we discuss the
complexified Ward identity in more detail. In particular we give a proof of the
complexified Ward identity directly from the Feynman rules in Feynman-Lorentz
gauge. Furthermore, we give more examples in calculating the one-line off-shell
currents using this technique.
