Abstract
The cellular aspect of space-time is introduced by replacing partial differentials with respect to position and time by partial central finite differences. A modified solution of the field equations for spinless mesons is then found in terms of the annihilation and creation operators of these particles. A form of the continuous-theory divergence theorem is found for the cellular case and this is used to obtain the cellular equivalent of the continuity equation for the charge-current density. In order that this equation be satisfied it is found that the definition of the charge-current density has to be modified by adding an extra term which turns out to be of the order of the square of the cell lengths. This term is calculated exactly for the charged-meson case.
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