Canonical transformations and the gauge dependence in general gauge theories

Gauge-invariant renormalizability is proven for a general gauge theory with an arbitrary gauge condition. It is shown that a canonical change of the variables in the initial effective action generates just a canonical change of the variables in the renormalized action and in the vertex generating functional. It is noted that the gauge condition enters the effective action as a canonical transformation. As a consequence, a change of the gauge condition is equivalent to the canonical transformation of the renormalized action and the vertex generating functional and this fact, in turn, leads to the gauge invariance of the renormalized S matrix