2025/10/07 by Gao, Ju, Shen, Fang
#FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2510.06016
The Aharonov--Bohm (AB) effect is conventionally interpreted as a phase shift acquired by charged particles encircling a flux, with no fields acting locally along their paths. Here we show that a confined Dirac electron exhibits a distinct AB coupling energy arising from a local current--potential interaction, whose form depends on the chosen prescription. In the wave--particle (WP) prescription the response is confined to the flux core: only the l=0 mode leaves a finite remnant as the core shrinks, while all higher modes vanish. In the wave--entity (WE) prescription the l=0 result coincides with WP, but for l ≥ 1 the response becomes a quantized, l--linear energy shift. The AB effect thereby emerges as a quantized, mode--resolved energy law that establishes locality through standard field coupling and distinguishes between electron prescriptions.