Gauge dependence of one-particle irreducible (1-PI) amplitudes in SU(N) Yang-Mills theory is shown to be generated by a canonical flow with respect to (w.r.t.) the extended Slavnov-Taylor (ST) identity, induced by the transformation of the gauge parameter under the BRST symmetry. For linear covariant gauges, the analytic expansion in the gauge parameter of 1-PI amplitudes is given in terms of coefficients evaluated in the Landau gauge and of derivatives w.r.t. the gauge parameter of the generating functional of the flow. An application to the gauge flow of the gluon propagator is considered.
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