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AUTHOR(S): Otto Laback
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TITLE On Invariant Potential Fields in Partially Occupied Charged Media |
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ABSTRACT In three-dimensional potential theory, classical analytic methods result in force fields exhibiting discontinuities, particularly at the boundary regions of volumes and surfaces occupied by charges and currents. Utilizing a specific topological structure introduced by E. Zeeman [1], I aim to augment the conventional methods of standard analysis, which are typically limited to differential and integral approaches. A specific bitopological structure in Euclidean space—namely the Zeeman topology Zpl with respect to the family of all piecewise linear arcs—is employed. The constructive proof of the non-regularity of this topology, along with the auto-homeomorphism group representing its invariance, provides the foundation for the physical applications presented here. We consider test particles on the boundary of a specific region occupied by charged particles. I propose an invariant solution that prioritizes force interactions restricted to straight lines over traditional coordinate invariance. |
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KEYWORDS invariant properties, special charges in potential theory, Zeeman topologies and applications |
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Cite this paper Otto Laback. (2026) On Invariant Potential Fields in Partially Occupied Charged Media. International Journal of Mathematical and Computational Methods, 11, 1-4 |
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