A Python lattice simulation showing emergent topological solitons

kisnorbert1 pts0 comments

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

Skip to main

You are using an outdated browser. Please upgrade your browser to improve your experience.

Service Incident: On 15 May 2026, between 12:25 and 13:11 GMT, Zenodo experienced an incident. The issue has been resolved. We apologize for the service disruption and any inconvenience caused. We will provide more details in the following days.

Published May 18, 2026

| Version v1

Preprint

Open

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 **

&copy; 2026, Norbert Levente Kis. All rights reserved. This document is licensed under CC<br>BY-NC-ND 4.0 International

Files

TRT_Kis_Norbert_Levente.pdf

Files<br>(316.2 kB)

Name<br>Size

Download all

TRT Particle simulator.html

md5:851f87351dca8c444866d3ed2da91f70

4.5 kB

Download

TRT Universe simulator.html

md5:061855531fd43b13e2f9bf1bcb1c872d

3.8 kB

Download

TRT_Kis_Norbert_Levente.pdf

md5:2f93560e69ee92047804a41612a07135

307.9 kB

Preview

Download

Views

Downloads

Show more details

All versions<br>This version

Views

Total views

Downloads

Total downloads

Data volume

Total data volume

0 Bytes<br>0 Bytes

More info on how stats are collected....

Versions

External resources

Indexed in

OpenAIRE

Communities

Keywords and subjects

Keywords

topological field theory

Yang--Mills theory

lattice gauge theory

quantum field theory

topological excitations

particle...

topological lattice final value energy theory

Related Articles