Abstract
This article represents a possible geometric interpretation of the Aharonov–Bohm (A–B) effect. We presented a new curve in the context of Einstein–Maxwell geometry, using the Bazanski approach. In the context of the geometrization philosophy, this curve can be used as an equation of motion of a charged test particle in a combined gravitational and electromagnetic field. The new equation of motion obtained contains two extra terms more than the geodesic equation. The first contains the electromagnetic field strength, while the second term gives rise to the electromagnetic potential. Both terms represent forces affecting the acceleration of the moving charged particle in the field mentioned above. The second term gives rise to the A–B effect. Linearization of the new equation gives more physical meaning to the extra terms obtained.
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Notes
BB are geometric quantities using which we can construct all objects of the geometry. For example, the BB of Riemannian geometry are the components of the metric tensor \(g_{\mu \nu }\).
A pure geometric treatment means, in general, that every physical quantity should be defined from the BB of the geometry used.
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Wanas, M.I., Kamal, M.M. & Ismail, Z.A. A pure geometric approach to the Aharonov–Bohm effect. Indian J Phys 95, 2865–2871 (2021). https://doi.org/10.1007/s12648-020-01926-w
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DOI: https://doi.org/10.1007/s12648-020-01926-w