 
Summary: J. Phys. A: Math. Gen. 31 (1998) 15631579. Printed in the UK PII: S03054470(98)883959
Gauge independence of the Smatrix in the causal
approach
Andreas Aste, G¨unter Scharf and Michael D¨utsch
Institut f¨ur Theoretische Physik der Universit¨at Z¨urich, Winterthurerstrasse 190, CH8057
Z¨urich, Switzerland
Institut f¨ur Theoretische Physik, Universit¨at Hamburg, Luruper Chaussee 149, D22761
Hamburg, Germany
Received 14 October 1997
Abstract. The gauge dependence of the timeordered products for YangMills theories is
analysed in perturbation theory by means of the causal method of Epstein and Glaser together
with perturbative gauge invariance. This approach allows a simple inductive proof of the gauge
independence of the physical Smatrix.
1. Introduction
The properties of (quantum) gauge invariance and gaugeparameter independence, which
are inherent in all kinds of gauge theories, have always been of great interest. In the
calculation of physical observables, i.e. Smatrix elements, the question of gauge parameter
independence arises automatically. In the usual Lagrangian approach to quantum field
theory, the gauge invariance of the classical Lagrangian has to be broken in order to quantize
the theory. Therefore, gauge fixing terms which depend on free gauge parameters are added
