In this thesis I study several applications of a maximally coupled QED model to particle interactions. The seminal work on the subject is Rosenbluth (1950), who studied the maximally coupled proton in electron-proton scattering. His analysis involves three assumptions which were starting points for the research reported here.

1. There was no derivation given (or referenced) for the maximally coupled vertex.
2. The dipole moment of the electron is ignored on the grounds that it is "quite small and decreases rapidly at higher energies".
3. He assumes that the proton is a distributed particle and attempts to fit his theoretical results using structure constants intended to reflect the details of the proton structure. I present a derivation of the maximally coupled vertex first used by Rosenbluth. The resultant vertex disagrees with that used by Rosenbluth (and all subsequent workers in the field) in the sign of the magnetic dipole parameter. I explore the ramifications of this discrepancy for the other two assumptions. Using the sign derived here for both the electron and the proton I show that the full maximally coupled cross-section to first order for electron-proton scattering to be in far better agreement with experiment than the commonly employed Rosenbluth model Further, at around 200 MeV the prediction developed here agrees with experiment to within the experimental uncertainties. At higher energies (and hence exchange momenta) this agreement falls away, however it is always in better agreement than the bare Rosenbluth expression. I show that for exchanged momentum of about the proton rest mass, the dipole-dipole terms are comparable to or larger than the monopole-monopole terms. Hence the dipole terms become more important as the exchanged energy increases. This is true for either vertex. Taking Rosenbluth's second assumption, but using the vertex derived here, I find little difference from the minimally coupled result. I discuss the difficulty of trying to re-develop the form factor approach of fitting the theoretical curves to experiment. I apply the maximally coupled QED model to neutron decay and obtain a neutron lifetime within 15% of the latest experimental value from a first order analysis involving no free parameters. Maximally coupled QED neutron-proton scattering is shown to account for about 10⁻⁴ of the measured scattering. This is as expected since this interaction is dominated by the strong nuclear force. I find poor agreement between the maximally coupled QED model and experiment for electron-neutron scattering. However, the application of a basically minimally coupled model for extracting electron-neutron scattering from the experimentally measured electron-deuteron scattering data is discussed and questioned. All of the two-photon scattering matrix elements for any two non-identical fermions are calculated, up to the integrations over the extra 4-momentum. These integrals are partially completed here, and all of the 4-space integrations are performed and presented. The development of a systematic approach to these integrals will allow their solution in later research.