Background field method: Alternative way of deriving the pinch technique’s results

We show that the background field method (BFM) is a simple way of deriving the same gauge-invariant results which are obtained by the pinch technique (PT). For illustration we construct gauge-invariant self-energy and three-point vertices for gluons at the one-loop level by the BFM and demonstrate that we get the same results which were derived via the PT. We also calculate the four-gluon vertex in the BFM and show that this vertex obeys the same Ward identity that was found with the PT.