The Gauged Faddeev-Niemi Soliton --- -Factor and Magnetic Moment

Title: The Gauged Faddeev-Niemi Soliton --- $g$-Factor and Magnetic Moment

Author: Alexander Novickis (alex.novickis@gmail.com)

The electron's gyromagnetic ratio $g = 2$ (before QED corrections) is among the most celebrated consequences of the Dirac equation and one of the sharpest tests of any electron model. For a composite soliton model to be viable, it must reproduce $g = 2$ --- not as a distinctive prediction, but as a necessary condition (any model failing it would be immediately ruled out). We show that the ungauged Faddeev-Niemi soliton, quantized via Adkins-Nappi-Witten (ANW) collective coordinates, generically gives $g \neq 2$: computed values range from $g = 2.12$ (monopole truncation) to $g = 9.67$ (full angular expansion), as expected for any extended charged object. However, when the soliton is coupled to a dynamical $U(1)$ gauge field --- the gauged Faddeev-Niemi Lagrangian in the Samoilenka-Shnir framework --- and quantized using the Finkelstein-Rubinstein procedure, all three hypotheses of the Belinfante-Rosenfeld theorem are satisfied: minimal coupling, Lorentz covariance, and spin-$\frac{1}{2}$. The theorem then guarantees $g = 2$ exactly. The non-trivial content is verifying that these hypotheses hold for an extended topological soliton after collective coordinate quantization, which is not automatic. The anomalous magnetic moment $a_e = (g - 2)/2 = \alpha/(2\pi)$ arises from one-loop radiative corrections in the low-energy effective theory, matching Schwinger's result, though the detailed matching between the gauged FN soliton and an effective Dirac field has not been established beyond leading order.

Keywords: gyromagnetic ratio, Faddeev-Niemi model, gauged soliton, Samoilenka-Shnir, Finkelstein-Rubinstein, magnetic moment, anomalous magnetic moment, Belinfante-Rosenfeld, Schwinger correction

Keywords: physics, soliton, topology, g factor, magnetic moment, Faddeev Niemi, gauged, Dirac, QED

DOI: 10.5281/zenodo.19111689

Series: Paper XLVII in the Hopf Soliton Programme