arXiv:2611.09311v1 Announce Type: new Abstract: The magnetic Aharonov--Bohm (AB) effect is often introduced through the idealised infinite solenoid and a complex scalar phase. We give a geometric-algebra formulation based on the compact toroidal magnets shielded by a superconductor employed in the electron-holography experiments of Tonomura and collaborators. Working in the real Euclidean Clifford algebra $ \mathrm{Cl}(3,0)$, we distinguish the unit volume pseudoscalar $I$ (grade 3), coordinate angles (scalars, grade 0), tangent vectors (grade 1), and directed surface bivectors (grade 2).
Quantum Research · 2026-11-09
A Geometric Journey Through the Aharonov--Bohm Effect: Tonomura's Toroid, Pseudoscalar Phase, and Quantum Holonomy in Clifford Algebra
arXiv:2611.09311v1 Announce Type: new Abstract: The magnetic Aharonov--Bohm (AB) effect is often introduced through the idealised infinite solenoid and a complex scalar phase. We give a geometric-algebra formulation based on the compact toroidal magnets shielded by a superconductor employed in the electron-holography experiments of Tonomura and collaborators.
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