What happens to conserved currents after spontaneos symmetry breaking?

[alemsalem]

should the current still be conserved? since it stills commutes with the Hamiltonian and symmetry is just hidden.

but I just read that the linear-σ model was invented to demonstrate how the axial current could be partially conserved?

Thanks!

 

[tom.stoer]

the axial current is not conserved due to the chiral anomaly; that's different from chiral symmetry breaking, b/c for spontaneous symmetry breaking the full charge operator still commutes with the Hamiltonian H, i.e. [H,Q] = 0, whereas for an anomaly the (renormalized) operator doesn't, i.e. [H,Q_A] ≠ 0!

http://en.wikipedia.org/wiki/Chiral_anomaly

 

[DrDu]

The Nobel lecture by Nambu is quite informative in this respect:
http://www.nobelprize.org/nobel_prizes/physics/laureates/2008/nambu_lecture.pdf