Four-fermion condensates and the higgs phenomenon

We stress that, in a gauge invariant description, the dynamical Higgs phenomenon for pure fermionic gauge theories is triggered by gauge singlet four-fermion condensates rather than gauge non-singlet quadratic ones. We propose criteria in order to select the actual four-fermion condensation channels. In some simple lattice gauge models at strong coupling, the existence of such condensates is shown to be related to the existence of a symmetry breaking potential for composite Higgs fields. In one of the models, we find the Higgs vacuum expectation value to be infinite, suggestive of a hierarchical pattern of symmetry breaking. (orig.)