A source of the divergences in QED is proposed, and a theory in which the Lamb shift and electron’s anomalous magnetic moment are calculated free of divergences is reviewed. It is shown that Dirac’s equation for a relativistic electron can be inferred from a Lorentz invariant having the form of the Lorentz gauge equation, , on identifying a carrier-wave energy  with the electron’s rest mass energy mc², the vector potential’s polarization vector with Pauli’s vector σ, and the envelops of the scalar and vector potentials with the four components of Dirac’s vector wave function. The same methodology is used to infer relativistic equations of motion having the Dirac form for a neutrino accompanied by ab initio neutrino-matter interaction terms. Then it is shown that the theory, which comprises Dirac’s equation plus the relativistic equations of motion for the neutrino, supports binding on a nuclear scale of energy and length. The experimentally observed weakness of the interaction energy of free neutrinos and matter is due to the smallness of the rate of tunnelling of free neutrinos through a potential barrier which exists in the interaction of free neutrinos and matter. Models are also proposed for the proton and neutron, and good agreement is obtained for the neutron-proton rest mass energy difference in view of the approximations made to solve the appropriate equations of motion.