Exploring resemblance between topological defects in liquid crystals and particle physics - gathered links and implementations. Jarek Duda, 2022
Basic idea (Manfried Faber, agreement with running coupling): define curvature of liquid-crystal-like field as EM field, this way Gauss law counts topological charge - leading to electromagnetism with built-in charge quantization, also repairing the problem of infinite energy of point charge.
Main article: https://arxiv.org/pdf/2108.07896
Light introduction with Mathematica sources: https://community.wolfram.com/groups/-/m/t/2856493
Slides: https://www.dropbox.com/s/9dl2g9lypzqu5hp/liquid%20crystal%20particles.pdf
Soliton slides: https://www.dropbox.com/s/aj6tu93n04rcgra/soliton.pdf
Talk: https://www.youtube.com/watch?v=od85ljeS4jA
liquid crystal particles-3Dequation and hedgehog.nb - derivation of 3D Maxwell-like equations, also ~Klein-Gordon for hedgehog ansatz
liquid crystal particles-4Dequation.nb - derivation of 4D equations, leading to addtional Maxwell equations for GEM ( https://en.wikipedia.org/wiki/Gravitoelectromagnetism )
Coulomb liquid crystal.nb - calculating effective potential for two topological charges by integrating energy density, getting Coulomb attraction/repulsion
Hedgehog Mathematica demonstration: https://demonstrations.wolfram.com/TopologicalChargesInBiaxialNematicLiquidCrystal/, of 2D interaction and phase evolution: https://demonstrations.wolfram.com/SeparationOfTopologicalSingularities/
