Which Loops Can Carry a Burgers Vector? Selection Rules on Non-Orientable Geometry
- 1Independent Researcher
Abstract
The strength of a dislocation is its Burgers vector: the circulation of the distortion field along a loop encircling the defect line. This article pursues a single question: what happens to this circulation when the carrier geometry is non-orientable? The answer reduces to one mechanism — the half-integer frequency lattice has no zero mode — and this mechanism yields the same selection rule on three successive rungs: at a point resolution the circulation is halved; along a curve with non-orientable normal bundle the longitudinal, Mobius-direction Burgers component cancels over two turns, confining the Burgers vector to span{t, e1}; on the surface rung the divisor term collapses under a triple selection to a single term (pi·A). The arenas are fixed by the Whitney formula (w1(N) = w1(M)|_Sigma + w1(Sigma)), among them the Euclidean arena: a non-orientable surface in R^4 with vanishing normal Euler number. The rules have a direct superconducting reading: a vortex is a phase dislocation, and the same gluing condition yields the half-quantum fluxoid physics measured on Mobius-type geometries. Every claim is verified by a deterministic, counter-checked script (16/16). The article extracts and assembles into a single whole the Burgers-selection story from the framework's published records.
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BibTeX
@misc{mark2026which,
title = {{Which Loops Can Carry a Burgers Vector? Selection Rules on Non-Orientable Geometry}},
author = {László Márk},
howpublished = {Zenodo (CERN European Organization for Nuclear Research)},
year = {2026},
month = aug,
doi = {10.5281/zenodo.21849262},
url = {https://doi.org/10.5281/zenodo.21849262},
note = {CC BY},
}
RIS
TY - UNPB
TI - Which Loops Can Carry a Burgers Vector? Selection Rules on Non-Orientable Geometry
AU - László Márk
PY - 2026
DA - 2026/08/08
PB - Zenodo (CERN European Organization for Nuclear Research)
DO - 10.5281/zenodo.21849262
UR - https://doi.org/10.5281/zenodo.21849262
AB - The strength of a dislocation is its Burgers vector: the circulation of the distortion field along a loop encircling the defect line. This article pursues a single question: what happens to this circulation when the carrier geometry is non-orientable? The answer reduces to one mechanism — the half-integer frequency lattice has no zero mode — and this mechanism yields the same selection rule on three successive rungs: at a point resolution the circulation is halved; along a curve with non-orientable normal bundle the longitudinal, Mobius-direction Burgers component cancels over two turns, confining the Burgers vector to span{t, e1}; on the surface rung the divisor term collapses under a triple selection to a single term (pi·A). The arenas are fixed by the Whitney formula (w1(N) = w1(M)|_Sigma + w1(Sigma)), among them the Euclidean arena: a non-orientable surface in R^4 with vanishing normal Euler number. The rules have a direct superconducting reading: a vortex is a phase dislocation, and the same gluing condition yields the half-quantum fluxoid physics measured on Mobius-type geometries. Every claim is verified by a deterministic, counter-checked script (16/16). The article extracts and assembles into a single whole the Burgers-selection story from the framework's published records.
ER -