Spontaneous symmetry breaking.- Goldstone theorem. Breaking gauge symmetries.- Higgs mechanism.- U(1) problem in QCD; a solution without instantons.- Gauge group topology and $\theta$ vacuum structure.

The book provides a non-perturbative approach to the symmetry breaking in the standard model, in this way avoiding the critical issues which affect the standard presentations. The debated empirical meaning of global and local gauge symmetries is clarified. The absence of Goldstone bosons in the Higgs mechanism is non-perturbatively explained by the validity of Gauss laws obeyed by the currents which generate the related

global gauge symmetry. The solution of the U(1) problem and the vacuum structure in QCD are obtained without recourse to the problematic semiclassical instanton approximation, by rather exploiting the topology of the gauge group.

Franco Strocchi is Senior Research Fellow of INFN (National Institute for Nuclear Research) in Pisa, Italy.