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An analysis of the self-energy problem for the electron in quantum electrodynamics Daykin, Philip Norman


The self-energy of the free electron at rest Is evaluated without the restriction that the self-interaction be a purely retarded interaction. Both the one-electron theory and the hole theory of the positron are treated. It is shown that in the one-electron theory the normally quadratically divergent transverse part of the self-energy vanishes if the self-interaction is assumed to be one half retarded plus one half advanced, the remaining Coulomb part of the self-energy being only linearly divergent. A similar theorem does not hold for the hole theory. A particular type of self-interaction leads to a vanishing self-energy in one-electron theory. However this does not solve the self-energy problem, as in this case radiation corrections to scattering will vanish as well. The self-energy of a bound electron is evaluated in a similar manner. The decay probability of an excited state is calculated as the imaginary part of the self-energy; the correct value is obtained only for a purely retarded self-interaction in hole theory. In the special case in which the external field is a uniform magnetic field, again only this interaction in hole theory gives the correct value for the anomalous magnetic moment. It is therefore concluded that any solution of the self-energy problem by introducing advanced self-interactions is to be ruled out.

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