Quantum electrodynamics based on self-fields, without second quantization: A nonrelativistic calculation of g-2

Using a formulation of quantum electrodynamics that is not second quantized, but rather based on self-fields, we compute the anomalous magnetic moment of the electron to first order in the fine-structure constant α. In the nonrelativistic (NR) case and in the dipole approximation, our result is $a_e$≡(g-2)/2=(4Λ/3m)(α/2π), where Λ is a positive photon energy cutoff and m the electron mass. A reasonable choice of cutoff, Λ/m=(3/4, yields the correct sign and magnitude for g-2 namely, $a_e$=+α/2π. In our formulation the sign of $a_3$ is correctly positive, independent of cutoff, and the demand that $a_e$=+α/2π implies a unique value for Λ. This is in contradistinction to previous NR calculations of $a_e$ that employ electromagnetic vacuum fluctuations instead of self-fields; in the vacuum fluctuation case the sign of $a_e$ is cutoff dependent and the equation $a_e$=α/2π does not have a unique solution in Λ.