How does dynamical mass generation work in field theory?

[matthias]

Can anyone tell me how dynamical mass generation works ?

what is effective mass?

thanks in advance

matt

 

[marlon]

Hi...

Dynamical mass-generation refers to the vacuum condensates in field theory...It can be shown that the perturbative vacuum is unstable and the vacuum energy can be lowered when certain condensates (the vacuum condensates) are created. These condensates do not exist (i mean, the expectation value of them is zero) when they are calculated with perturbation theory. They reason for this is that symmetry of the physical models at hand do not allow a non-zero expectation value. In a non-perturbative field theory (like low energy-QCD) these condensates DO occur and as a consequence of this some symmetries of the models are broken. When symmetry is broken, mass is generated through the Higgs-mechanism. These condensates are thus responsible for giving massless-elementary particles some dynamically generated mass. For example the QCD Lagrangian contains massless quarks and exhibits as a consequence of this chiral symmetry. When vaccuumcondensates are allowed (low-energies or non-perturbative QCD) these quark-antiquarkpairs will break this chiral symmetry and will give the quars mass.

Effective mass is a concept that QFT took over from solid state physics. As an example : consider many electrons that interact with each other. This is one many-particle system with many coupled differential equations. We cannot solve this so what's the way out? Well take one electron and put all the "interactions" it makes with the surrounding electrons into the mass of the electron. What we get is the equation of motion (with adapted mass = effective mass)of an electron that moves around in the vaccuum, because all the interactions with neighbors are put into the effective mass. basically what you have done here is convert one many-body problem into many one body problems that we CAN solve...

Keep in mind that this is a simplified picture but it gives you an image...An effective field theory is a field theory of which the degrees of freedom are not elementary. For example , the degrees of freedom of QCD are quarks, which are elementary particles. In QHC, the degrees if freedom are hadrons (particles that consist out of quarks and feel the strong force), but they are not elementary since they are built out of quarks...

Particles are elementary when they can be used as a FUNDAMENTAL representation of the symmetry-group of the Lagrangian of the field theory...Like quarks with three colours form the fundamental representation of SU(3), the local colour symmetry of QCD which generates 8 gauge bosons (you know, the gluons...)

regards
marlon