Quantum Electrodynamics Based on Self-fields, Without Second Quantization: A Nonrelativisitc Calculation of g – 2

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American Physical Society

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https://scholarsarchive.byu.edu/facpub/1850; https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=2876&context=facpub
Barut, A. O.; Dowling, Jonathan P.; Van Huele, Jean F.
American Physical Society
quantum electrodynamics; self-fields; nonrelativistic; Physics; Quantum Physics
article description
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=(4Λ/3m)(α/2π), where Λ is a positive photon energy cutoff and m the electron mass. A reasonable choice of cutoff, Λ/m=¾, yields the correct sign and magnitude for g—2 namely, ae=+α/2π. . In our formulation the sign of a3 is correctly positive, independent of cutoff, and the demand that ae=+α/2π 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/2π does not have a unique solution in Λ.