Feynman, R.P.; A Relativistic Cut-Off for Classical Electrodynamics
Phys. Rev. 74 (1948) 939;

Abstracts
Ordinarily it is assumed that interaction between charges occurs along light cones, that is, only where the four-dimensional interval s^{2} = t^{2} - r^{2} is exactly zero. We discuss the modifications produced if, as in the theory of F. Bopp, substantial interaction is assumed to occur over a narrow range of s^{2} around zero. This has no practical effect on the interaction of charges which are distant from one another by several electron radii. The action of a charge
on itself is finite and behaves as electromagnetic mass for accelerations which are not excessive. There also results a classical representation of the phenomena of pair production in sufficiently strong fields.

Related references See also M. Born and L. Infeld, Proc. Roy. Soc. A144 (1934) 425;
P. A. M. Dirac, Proc. Roy. Soc. A167 (1938) 148;
C. J. Eliezer, Rev. of Mod. Phys. 19 (1947) 147;
N. Rosen, Phys. Rev. 72 (1947) 298;
F. Bopp, Annalen der Physik. Leipzig 42 (1942) 573;
B. Podolsky and P. Schwed, Rev. of Mod. Phys. 20 (1948) 40;
J. A. Wheeler and R. P. Feynman, Rev. of Mod. Phys. 17 (1945) 157;

Record comments
Proposal to modify classical electrodynamics to a form suitable for quantization.