GAUGE-INVARIANCE OF GREEN-FUNCTIONS - BACKGROUND-FIELD METHOD VERSUS PINCH TECHNIQUE

Application of the background-field method to QCD and the electroweak Standard Model yields gauge-invariant effective actions giving rise to simple Ward identities. Within this method, we calculate the quantiti es that have been treated in the literature using the pinch technique. Putting the quantum gauge parameter equal to one, we recover the pinc h-technique results as a special case of the background-field method. The one-particle-irreducible Green functions of the background-field m ethod fulfil for arbitrary gauge parameters the desirable theoretical properties that have been noticed within the pinch technique. Therefor e the background-field formalism provides a general framework for the direct calculation of well-behaved Green functions. Within this formal ism, the pinch technique appears as one of arbitrarily many equivalent possibilities.