Canonical transformations and the gauge dependence in general gauge theories

Abstract

A proof is given of the gauge-invariant renormalizability of general gauge theories in arbitrary gauges. We show that a canonical change of variables in the initial effective action also generates only a canonical change of variables in the renormalized action and in the vertex generating functional. We note that the gauge condition enters into the effective action as a canonical transformation. As a consequence, changing the gauge condition is equivalent to a canonical transformation of the renormalized action and the vertex generating functional. This, in turn, implies the gauge invariance of the renormalized S matrix.