Preface to the Third Edition
The main motivation for having this third edition is the addition of an Appendix
which deepens and clarifies some of the concepts introduced and developed in the
core text. In the discussion of the breaking of continuous symmetries, the crucial
point of the dynamical delocalization of the relevant variables does not seem to be
sufficiently emphasized in the literature. Its impact on the local generation of a
continuous symmetry, at the basis of Goldstone theorem, has been discussed in
Part II, Sect. 25.2, but, in our opinion, this argument deserves more consideration,
since the Coulomb delocalization is the critical one and, as such, affects most
many-body systems and gauge theories of elementary particles. The main consequence is the key role of the boundary conditions which give rise to volume effects,
in contrast with the standard case described by (essentially) local dynamical variables. The relevant physical result is the occurrence of energy gaps associated to the
spontaneous breaking of continuous symmetries, in contrast with the Goldstone
theorem. Examples are the Anderson model of superconductivity (close to the
molecular field approximation of the Heisenberg model), the electron gas in uniform background (with the plasmon energy gap derived by the breaking of the
Galilei group), the Higgs mechanism in the Coulomb gauge.
Other sections of the Appendix deal with the consequences and breaking of
global gauge symmetries. Invariance under a local gauge symmetry is critically
reviewed versus the validity of a local Gauss law on the physical states. This is
argued to be the relevant property responsible for important physical properties like
the Higgs mechanism in electroweak interactions, the topological group and the
chiral symmetry breaking in quantum chromodynamics.
In line with the approach adopted in the previous editions, attention is paid to the
main ideas and to the questions of principle leaving to the interested reader the task
and duty of further developing the technical mastership.
Lastly, this new edition benefits from the correction of misprints and some
refinements of the main text.
Pisa, Italy
Franco Strocchi
v
The main motivation for having this third edition is the addition of an Appendix
which deepens and clarifies some of the concepts introduced and developed in the
core text. In the discussion of the breaking of continuous symmetries, the crucial
point of the dynamical delocalization of the relevant variables does not seem to be
sufficiently emphasized in the literature. Its impact on the local generation of a
continuous symmetry, at the basis of Goldstone theorem, has been discussed in
Part II, Sect. 25.2, but, in our opinion, this argument deserves more consideration,
since the Coulomb delocalization is the critical one and, as such, affects most
many-body systems and gauge theories of elementary particles. The main consequence is the key role of the boundary conditions which give rise to volume effects,
in contrast with the standard case described by (essentially) local dynamical variables. The relevant physical result is the occurrence of energy gaps associated to the
spontaneous breaking of continuous symmetries, in contrast with the Goldstone
theorem. Examples are the Anderson model of superconductivity (close to the
molecular field approximation of the Heisenberg model), the electron gas in uniform background (with the plasmon energy gap derived by the breaking of the
Galilei group), the Higgs mechanism in the Coulomb gauge.
Other sections of the Appendix deal with the consequences and breaking of
global gauge symmetries. Invariance under a local gauge symmetry is critically
reviewed versus the validity of a local Gauss law on the physical states. This is
argued to be the relevant property responsible for important physical properties like
the Higgs mechanism in electroweak interactions, the topological group and the
chiral symmetry breaking in quantum chromodynamics.
In line with the approach adopted in the previous editions, attention is paid to the
main ideas and to the questions of principle leaving to the interested reader the task
and duty of further developing the technical mastership.
Lastly, this new edition benefits from the correction of misprints and some
refinements of the main text.
Pisa, Italy
Franco Strocchi
v