Gauge-invariant Green's functions for the bosonic sector of the standard model

Abstract

There are many applications in gauge theories where the usually employed framework involving gauge-dependent Green's functions leads to considerable problems. In order to overcome the difficulties invariably tied to gauge dependence, we present a manifestly gauge-invariant approach. We propose a generating functional of appropriately chosen gauge-invariant Green's functions for the bosonic sector of the standard model. Since the corresponding external sources emit one-particle states, these functions yield the same S-matrix elements as those obtained in the usual framework. We evaluate the generating functional for the bosonic sector of the standard model up to the one-loop level and carry out its renormalization in the on-shell scheme. Explicit results for some two-point functions are given. Gauge invariance is manifest at any step of our calculation.