Abstract
Whether the spin-1/2 Aharonov-Bohm Hamiltonian supports bound states has remained controversial since Hagen concluded that no such states exist for a Dirac particle. Here, we show that Hagen's solution corresponds to a particular member of the one-parameter family of self-adjoint extensions that describe the singular Zeeman interaction, and we identify which member the microscopic physics selects. Matching the extension parameter to a finite-radius flux tube yields $ν=0$ precisely at $g=2$, and it does so in every flux sector. The critical $g$ factor is therefore universal, $g_c=2$, and depends on neither the flux sector nor the regularization radius. The flux sector controls the depth of the bound state energy, and we obtain a closed-form expression showing that binding deepens markedly with the integer part of the flux. Hagen's conclusion is thus confirmed and sharpened: it is not a statement about one arbitrary member of a family of extensions, but about the member that the physics selects when the magnetic moment takes its Dirac value, and an anomalous moment is a necessary and sufficient condition for binding in the singular channel.
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Cite this article
APA 7
Salem, V., Silva, E. O., & Andrade, F. M. (2026). Universal critical $g$ factor for spin-1/2 Aharonov-Bohm bound states. https://omanscience.com/en/articles/universal-critical-g-factor-for-spin-1-2-aharonov-bohm-bound-states
MLA 9
Salem, Vinícius, et al. "Universal critical $g$ factor for spin-1/2 Aharonov-Bohm bound states." https://omanscience.com/en/articles/universal-critical-g-factor-for-spin-1-2-aharonov-bohm-bound-states.
Chicago (author–date)
Salem, Vinícius, Edilberto O. Silva, and Fabiano M. Andrade. 2026. "Universal critical $g$ factor for spin-1/2 Aharonov-Bohm bound states." https://omanscience.com/en/articles/universal-critical-g-factor-for-spin-1-2-aharonov-bohm-bound-states.
Harvard
Salem, V., Silva, E. O. and Andrade, F. M. (2026) 'Universal critical $g$ factor for spin-1/2 Aharonov-Bohm bound states', Available at: https://omanscience.com/en/articles/universal-critical-g-factor-for-spin-1-2-aharonov-bohm-bound-states.
Vancouver
Salem V, Silva EO, Andrade FM. Universal critical $g$ factor for spin-1/2 Aharonov-Bohm bound states. https://omanscience.com/en/articles/universal-critical-g-factor-for-spin-1-2-aharonov-bohm-bound-states
IEEE
V. Salem, E. O. Silva, and F. M. Andrade, "Universal critical $g$ factor for spin-1/2 Aharonov-Bohm bound states," https://omanscience.com/en/articles/universal-critical-g-factor-for-spin-1-2-aharonov-bohm-bound-states.