reggepole said:
When does the process of breaking take place? After or before some small perturbation appears? BTW I read somewhere that this effect does not appear in quantum mechanics.
Let me answer the second question first. Suppose you have a potential V( \phi) that reaches minimal value for two distinct non zero field values.
If you replace the field by its opposite value (reflection symmetry), the Lagrangian stays the same but once you calculated the two minima, you go from one to the other by replacing the field by its opposite.
In QM, the particle will tunnel between the two minima and the probablity of being in one of the two vacua is equal because of reflection symmetry of the hamiltonian. In QFT, the tunneling barrier is infinite (this is proven in QFT) and extends over the entire volume of the system. Thus, one of the two minima must be chosen. By chosing one of them, you are breaking the symmetry because if you replace the field by its opposite you will no longer be able to go to the other potential minimum, hence reflection symmetry is lost. This answers your first question : the breakdown takes place once nature has chosen one out of all possible vacuum values (this happens prior to the excitations).
once you have one minimum, you study the excitations from this vacuum configuration and you will see that extra terms will arise in the equations of motion that express the interaction of an elementary particle with a certain boson (ie the Higgs particle). It is this interaction that gives mass to elementary particles.
In order to make sure this will work, you need to adapt the potential in the Lagrangian in such a way that you are sure the associated vacuum value will be degenerate so that breakdown can take place.
regards
marlon
PS in QFT you can go from one minimum to another by going from one gauge configuration at negative spatial infinity to another at positive spatial infinity. Particles that do this are called instantons.
