Abstract
IN free space the electromagnetic potential φµ of Maxwell's equations is related to the sources of the field jµ by the equation □φµ = jµ. If the source of the field is an arbitrarily moving charge, the retarded solution for φµ may be expressed as an integral over the world line of the charge (zµ = zµ (τ)): where Dret is the four-dimensional retarded Green's function. Concise expressions for the fields Fµν = φµ,ν − φν,µ can then be obtained by differentiating under the integral sign in (1). The same processes may be applied to the calculation of the radiation fields Fµνrad = Fµνret − Fµνadv (by changing the Green's function) and the method affords an effective means of evaluating the radiation field on the world line of the charge1. The latter fields have the value:
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References
Thirring, W. E., Principles of Quantum Electrodynamics (Academic Press Inc., 1958).
Ellis, J. R. (to be published).
Ward, G. N., Proc. Roy. Soc. London, A, 279, 562 (1964).
Ellis, J. R., Proc. Camb. Phil. Soc., 59, 759 (1963).
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ELLIS, J. Fields of Moving Multipoles. Nature 205, 582 (1965). https://doi.org/10.1038/205582a0
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DOI: https://doi.org/10.1038/205582a0
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