Quantum electrodynamics based on self-fields, without second quantization: A nonrelativistic calculation ofg-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 aₑ{≡}(g-2)/2=(4{Λ}/3m)({α}/2{π}), 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, aₑ=+{α}/2{π}. In our formulation the sign of a₃ is correctly positive, independent of cutoff, and the demand that aₑ=+{α}/2{π} implies a unique value for {Λ}. This is in contradistinction to previous NR calculations of aₑ that employ electromagnetic vacuum fluctuations instead of self-fields; in the vacuum fluctuation case the sign of aₑ is cutoff dependent and the equation aₑ={α}/2{π} does not have a unique solution in {Λ}.