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In the arena of the discrete phase space and continuous time, the theory ofS-marix is formulated. In the special case of Quantum-Electrodynamics (QED),the Feynman rules are precisely developed. These rules in the fourmomentum turnout to be identical to the usual QED, except for the vertex function. The newvertex function is given by an infinite series which can only be treated in anasymptotic approximation at the present time. Preliminary approximations provethat the second order self-energies of a fermion and a photon in the discretemodel have convergent improper integrals. In the final section, a sharperasymptotic analysis is employed. It is proved that in case the number ofexternal photon or fermion lines is at least one, then the S-matrix elementsconverge in all orders. Moreover, there are no infra-red divergences in thisformulation.

Discrete phase space - III: The Divergence-free S-matrix elements