Summary: J. Phys. A: Math. Gen. 30 (1997) 57855792. Printed in the UK PII: S0305-4470(97)82202-0
On gauge invariance and spontaneous symmetry breaking
A Aste, G Scharf and M D¨utsch
Institut f¨ur Theoretische Physik der Universit¨at Z¨urich, Winterthurerstrasse 190, CH-8057
Institut f¨ur Theoretische Physik der Universit¨at Hamburg, Luruper Chaussee 149, D-22761
Received 27 February 1997, in final form 28 May 1997
Abstract. We show how the widely used concept of spontaneous symmetry breaking can be
explained in causal perturbation theory by introducing a perturbative version of quantum gauge
invariance. Perturbative gauge invariance, formulated exclusively by means of asymptotic fields,
is discussed for the simple example of Abelian U(1) gauge theory (Abelian Higgs model). Our
findings are relevant for the electroweak theory, as pointed out elsewhere.
It is quite a common assumption that scalar QED with massive photons is not a gauge
theory in the usual sense, because the introduction of a mass term in the Lagrangian for
the gauge field violates the classical gauge invariance of the theory. Therefore, a `Higgs'
field with a nonvanishing vacuum expectation value is usually coupled to the photon which
then acquires a mass . Proceeding in this way, the local U(1) invariance is not absent,