High Precision Determination of α and Quantum Electrodynamics for Nonrelativistic Systems

New measurements of the anomalous magnetic moment of the electron and the corresponding theoretical calculation have reached the precision exceeding 4 × 10^-9 and 7 × 10^-9, respectively. This enables us to determine the fine structrure constant α to a precision of 8 × 10^-9. For comparison, the best measurements of α based on the ac Josephson effect and quantized Hall effect have uncertainties of 56 × 10^-9 and 24 × 10^-9, respectively. These values of α disagree by more than two standard deviations from each other. One possible source of the discrepancy is nonrelativistic quantum mechanics itself, in which the interaction with the radiation field is not properly defined. We have explored the possibility of replacing it with a low-energy adaptation of quantum electrodynamics which treats large and small length scales differently following the renormalization group concept. This formulation enables us to close a loophole in the usual argument for the exactness of ac Josephson and quantized Hall effects. It may also serve as a practical starting point for calculating theoretical corrections to these effects.