Theoretical analysis quantifies charge radius in electrons and neutrons, indicating connections to electromagnetic properties.
We extend the topological particle framework of Discrete Topological Torsion Theory (DTTT), in which fundamental particles are knotted solitons in a Cosserat elastic vacuum, to derive the electromagnetic properties of the electron and neutron. Our central result is a theorem showing that fractional electric charges emerge necessarily from the torus knot parameters: for the trefoil T(2,3), the q=3 meridional winding quantises charge in units of e/3 while the isospin doublet constraint uniquely selects the lobe charges +2e/3,−e/3 precisely the quark model values, derived here without reference to quarks or QCD. This charge quantisation and the electromagnetic coupling α−1=137.036 are two consequences of a single Boundary Representation Theorem on the peripheral torus. The electron, classified as an unknot (nT=0), has no topologically stabilised charge radius, consistent with experimental bounds re<10−18 m. For the neutron, the trilobular charge asymmetry yields ⟨rE2⟩n<0 with the correct sign (DERIVED). We introduce the Sachs-Dirac-Foldy decomposition to separate the model-independent Foldy contribution from the intrinsic Dirac radius.
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Aaditya Bhatt (2026) studied this question.
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