Universal critical g factor for spin-1/2 Aharonov-Bohm bound states
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, gc=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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BibTeX
@misc{salem2026universal,
title = {{Universal critical $g$ factor for spin-1/2 Aharonov-Bohm bound states}},
author = {Vinícius Salem and Edilberto O. Silva and Fabiano M. Andrade},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08521},
eprint = {2610.08521},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08521},
}
RIS
TY - UNPB
TI - Universal critical g factor for spin-1/2 Aharonov-Bohm bound states
AU - Vinícius Salem
AU - Edilberto O. Silva
AU - Fabiano M. Andrade
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08521
UR - https://arxiv.org/abs/2610.08521
AB - 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.
ER -