# On a New, Finite, “Charge-Field” Formulation of Classical Electrodynamics

## Abstract

The “charge-field” approach to electrodynamic processes is based on the paradigm that charges and their associated electromagnetic fields are permanently connected in elementary charge-field functional structures, with physical processes being described by the interactions between various charge-field entities in the system. The new formulation of interest to us here, called classical elementary measurement electrodynamics (CEMED),^{(1)} resembles Maxwell-Lorentz theory in that the fields connected to each charge are not eliminated, but differs in that each charge carries its *own* Maxwell field equation (i.e., *N* charges and *N* Maxwell “charge-fields,” *each* with its *own* Maxwell field equation, and requiring its *own* independent set of boundary conditions). It resembles a direct-action theory in that only interparticle interactions play a role in the formalism, with no self-Coulomb interactions at the classical level, and that all free fields uncoupled to charges are absent from the theory. However, it differs from standard Fokker-type direct-action theories^{(2)} in that the coupled fields are still present, i.e., not eliminated *a priori* as dynamical variables. The reason this can be done is that the Maxwell field equations (one for each charged particle) are treated like identities which prescribe how fields are functionals of the currents (i.e., the Maxwell equations are treated like constraints on the particle dynamics, with free fields playing no role in the formalism since they don’t represent an interaction between charges). This direct (charge-field) action formalism with the requirements of positive definite energy and causality^{(3)} yields a theory which is in complete agreement with that of renormalized Maxwell-Lorentz theory but without any infinite renormalizations being required.

## Keywords

Quantum Electrodynamic Free Field Interparticle Interaction Classical Electrodynamic Conservation Identity## Preview

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## References and Notes

- 1.
- 2.For a particularly lucid discussion of Fokker-type theories see W. Panofsky and M. Phillips,
*Classical Electrodynamics*, 2nd ed., Addison-Wesley, Reading, Massachusetts (1962).Google Scholar - 3.By “causality” we will specifically mean the presence of “mutual” retarded electromagnetic charge-fields (see the second reference quoted in footnote 1 above); however, charge-field “radiation’
^{.}can still contain ”advanced“ components.Google Scholar - 4.
- 5.Darryl Leiter,
*Nuovo Cimento B***48**, 15 (1978); On the quantum electrodynamics of mutually interacting charge-fields: A new approach to photon quantization in electron-positron processes.Google Scholar