Gauge invariance, gauge-parameter independence and properties of Green functions

Abstract

The application of the background-field method to the electroweak Standard Model is reviewed and further explored. Special emphasis is put on questions of gauge invariance and gauge-parameter (in-)dependence. Owing to the gauge invariance of the background-field effective action, the vertex functions obey simple Ward identities which imply important properties of the vertex functions. Carrying out the renormalization in a way respecting background-field gauge invariance leads to considerable simplifications. The generalization of the background-field method to the non-linear realization of the scalar sector of the Standard Model is illustrated. Furthermore, the interplay between gauge independence of the S-matrix and Ward identities of vertex functions is investigated. Finally, the Standard Model contributions to the $S$, $T$, and $U$ parameters are calculated and discussed within the background-field method.

25 pages, latex, ps-file available via anonymous ftp from ftp://ftp.physik.uni-wuerzburg.de/pub/preprint/WUE-ITP-95-010.ps , to appear in the proceedings of the Ringberg Workshop ``Perspectives for electroweak interactions in $e^+e^-$ collisions'', Ringberg Castle, February 5-8, 1995