On a Dynamical Origin for Fermion Generations

We investigate a proposal to address several outstanding shortcomings of the perturbative Standard Model (SM) of particle physics. The appeal of this proposal is that these features are a manifestation of the non-perturbative sector of the SM, requiring no assumptions about new physics beyond presently attainable experimental limits. In this thesis we apply non-perturbative techniques to two complementary models: a toy 4-fermion model containing explicit chiral symmetry-breaking terms and the quenched hypercharge gauge interaction. Understanding of how fermion mass, generations and CP-violation might arise is first investigated in the toy 4-fermion model. It is shown that different scale-invariant 4-fermion operators are present for the three subspaces of the full theory, enabling self-consistent introduction of three fermion generations. The second part of the thesis is concerned with dynamical fermion mass generation in the quenched hypercharge interaction. In particular we follow the successful procedure developed for QED, developing a 1-loop renormalisable vertex {\it ansatz} for solution of the fermion self-energy Dyson-Schwinger equation. We find two mass "gaps", possibly corresponding to two types of scalar 4-fermion pairing. These "gaps" cannot, however, be interpreted as physical fermion mass. An alternative possibility, that of a rearrangement of fermionic degrees of freedom analogous to spin-charge separation in condensed matter physics, is also briefly outlined