On the electron self-energy

Abstract.

Previously, we have shown that the anti-de Sitter vacuum produced by a negative cosmological constant $\Lambda\equiv -A$ gives rise to an effective mass term in the curved-space Dirac equation for the spinor wave function $\psi$ due to Fock, in which the contribution from the spinorial affine connection is ${\rm i}\gamma^{j}\Gamma_{j} = m\gamma^{0}$, where $m=\sqrt{3 A}/2$. Here, this result is used to construct an extended model of the electron interior that is divergence-free, singularity-free and locally Lorentz invariant, and yields the approximate value $r_{\rm a}\approx 6.1 \times 10^{-26}$ cm for the radius of the charge cloud, assuming the total gravitational energy $E\approx 8\pi r_{\rm a}^{3}A/3\kappa^{2}$ to be in the form of vacuum fluctuations and to constitute the rest-mass energy m. The model is discussed further with regard to the phenomenon of “Zitterbewegung”, while the Hamiltonian operator formalism due to Born and Jordan is consistent with the wave equation, although the gamma matrices $\gamma_{i}$ are time dependent. The theory is effectively invariant under T, C and P, since the metric g_ij differs from Minkowski only by a factor $\lesssim 10^{-30}$, and is thus compatible with the most recent experimental limits on the electric dipole moment of the electron d_e obtained from polar molecules, which indicate that $\vert d_{\rm e}\vert \lesssim 10^{-28} e {\rm cm} \approx 2\times 10^{-3} r_{\rm a} e$.