Final Energy: 223.1049Initial Topological Value: 524249.3288 -> Final Topological Value: 524088.1205Execution Time: 295.26 seconds ** Process exited - Return Code: 0 ** © 2026, Norbert Levente Kis. All rights reserved. This document is licensed under CCBY-NC-ND 4.0 International" />
Final Energy: 223.1049Initial Topological Value: 524249.3288 -> Final Topological Value: 524088.1205Execution Time: 295.26 seconds ** Process exited - Return Code: 0 ** © 2026, Norbert Levente Kis. All rights reserved. This document is licensed under CCBY-NC-ND 4.0 International" />
Final Energy: 223.1049Initial Topological Value: 524249.3288 -> Final Topological Value: 524088.1205Execution Time: 295.26 seconds ** Process exited - Return Code: 0 ** © 2026, Norbert Levente Kis. All rights reserved. This document is licensed under CCBY-NC-ND 4.0 International" />
Topological Relativity Theory: A Quantum Gauge Field Framework for Particle Generations and Emergent Couplings
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Published May 18, 2026
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Topological Relativity Theory: A Quantum Gauge Field Framework for Particle Generations and Emergent Couplings
Authors/Creators
Kis, Norbert Levente
Description
I construct a topological field framework in which particles arise as gauge-coupled con-<br>figurations of a single fundamental field. The model extends earlier scalar constructions<br>by introducing an explicit Yang–Mills sector. To obtain a well-defined non-perturbative<br>description, the theory is formulated on a lattice, where gauge consistency and numerical<br>stability are maintained. The classical dynamics is examined through gradient flow. It is<br>found that purely classical configurations do not lead to stable soliton solutions. However,<br>in the lattice Yang–Mills formulation, localized configurations persist and exhibit a discrete<br>spectrum of fluctuations. The eigenvalue spectrum of the fluctuation operator provides a<br>natural ordering of modes. This structure gives rise to a hierarchical pattern which may be<br>associated with fermion generations. Furthermore, a summation over the spectrum repro-<br>duces the general scale and behavior of the fine structure constant. The analysis indicates<br>that stability cannot be achieved at the classical level alone. Quantum corrections must be<br>taken into account. At one-loop order, the effective action introduces additional terms which<br>modify the energy functional and may stabilize the configuration. The results suggest that<br>particles are not classical solitons, but rather quantum excitations of topologically nontrivial<br>gauge-field configurations.
The scale-dependence of the topological conservation law was explicitly verified by scaling the lattice volume from $N=6$ to $N=64$. While un-regularized small-lattice flows exhibit severe topological leakage ($\Delta Q / Q \sim 10\%$), the high-resolution $64^3$ simulation yields an asymptotic freezing of the topological charge. With a relative variance of $\Delta Q / Q \approx 0.03\%$ alongside continuous energy relaxation ($\Delta E ), the system provides robust numerical evidence of emergent topological solitons in the classical gauge sector prior to quantum loop corrections.
$6 \times 6 \times 6$ lattice: 10% decay (severe leakage)
$40 \times 40 \times 40$ lattice: 0.065% decay (near-perfect conservation)
$64 \times 64 \times 64$ lattice: 0.030% decay (even closer to pure zero)
Simulation starting on a 64x64x64 lattice...<br>Step: 50/200 completed...<br>Step: 100/200 completed...<br>Step: 150/200 completed...<br>Step: 200/200 completed...
--- RESULTS ---<br>Initial Energy: 232.0273 -> Final Energy: 223.1049<br>Initial Topological Value: 524249.3288 -> Final Topological Value: 524088.1205<br>Execution Time: 295.26 seconds
** Process exited - Return Code: 0 **
© 2026, Norbert Levente Kis. All rights reserved. This document is licensed under CC<br>BY-NC-ND 4.0 International
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topological field theory
Yang--Mills theory
lattice gauge theory
quantum field theory
topological excitations
particle...