Dynamic Mass Generation for Fermions

Abstract

Fermionic mass is commonly represented in Lagrangian field theories either by direct mass terms or by Yukawa couplings to scalar fields which have the potential to develop non-zero expectation values. Both types involve a priori undetermined parameters. In gauge theories there arises the further problem of explaining why some of the fermions are relatively light (the gauge hierarchy problem [1]). The purpose of this note is to suggest a mechanism, appropriate to a class of gauge theories, which might go some way to solving these problems. Our considerations, though couched for a particular group, are more generally applicable.