Quantum electrodynamics between conducting plates III. Relativistic theory and magnetic moment of the free electron

We calculate the change $\Delta \mu $ in the radiative correction to the magnetic moment $\mu $ of a free electron, when the electron is inserted between infinite perfectly conducting parallel plates. The order of magnitude is given by $\delta \mu /\mu \sim \alpha \not\!\lambda /L$, with $\alpha $ the fine structure constant, $\not\!\lambda $ the Compton wavelength, and L the plate separation. This contrasts with a bound electron, for which the preceding paper found $\delta \mu /\mu \approx \alpha (\not\!\lambda /L^{2})$. Since a relativistic field theory calculation is essential for $\delta \mu $, we obtain as a by-product a relativistic confirmation of the leading spin-independent energy shifts for a free electron, reported in an earlier paper.