  We review the usual account of the phenomena of spontaneous symmetry breaking
(SSB), pointing out the common misunderstandings surrounding the issue, in
particular within the context of quantum field theory. In fact, the common
explanations one finds in this context, indicate that under certain conditions
corresponding to the situation called SSB, the vacuum of the theory does not
share the symmetries of the Lagrangian. We explain in detail why this statement
is incorrect in general, and in what limited set of circumstances such
situation could arise. We concentrate on the case of global symmetries, for
which we found no satisfactory exposition in the existing literature, and
briefly comment on the case of gauge symmetries where, although insufficiently
publicized, accurate and complete descriptions exist. We briefly discuss the
implications for the phenomenological manifestations usually attributed to the
phenomena of spontaneous symmetry breaking, analyzing which might be affected
by our analysis and which are not. In particular we describe the mass
generation mechanism in a fully symmetric scheme (i.e., with a totally
symmetric vacuum), and briefly discuss the implications of this analysis to the
problem of formation of topological defects in the early universe.
