Physics – Mathematical Physics
Scientific paper
2006-07-11
J.Phys.A40:3173-3188,2007
Physics
Mathematical Physics
Invited contribution to ``The Quantum Universe'', dedicated to G. Ghirardi for his 70th birthday
Scientific paper
10.1088/1751-8113/40/12/S17
The violation of the Noether relation between symmetries and charges is reduced to the time dependence of the charge associated to a conserved current. For the U(1) gauge symmetry a non-perturbative control of the charge commutators is obtained by an analysis of the Coulomb charged fields. From this, in the unbroken case we obtain a correct expression for the electric charge on the Coulomb states, its superselection and the presence of massless vector bosons; in the broken case, we obtain a general non-perturbative version of the Higgs phenomenon, i.e. the absence of massless Goldstone bosons and of massless vector bosons. The conservation of the (gauge dependent) current associated to the U(1) axial symmetry in QCD is shown to be compatible with the time dependence of the corresponding charge commutators and a non-vanishing eta' mass, as a consequence of the non locality of the (conserved) current.
Morchio Giovanni
Strocchi Franco
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