Discrete physics: Practice, representation and rules of correspondence

We make a brief historical review of some aspects of modern physics which we find most significant in our own endeavor. We discuss the ''Yukawa Vertices'' of elementary particle theory as used in laboratory practice, second quantized field theory, analytic S-Matrix theory and in our own approach. We review the conserved quantum numbers in the Standard Model of quarks and leptons. This concludes our presentation of the ''E-frame.'' We try to develop a self-consistent representation of our theory. We have already claimed that this approach provides a discrete reconciliation between the formal (representational) aspects of quantum mechanics and relativity. Also discussed are rules of correspondence connecting the formalism to the practice of physics by using the counter paradigm and event-based coordinates to construct relativistic quantum mechanics in a new way. 31 refs., 12 figs., 1 tab