This is STM image of hexagonal lattice of graphene, here on right side is STM image for semiconductor instead (source: http://www.phy.bme.hu/~zarand/LokalizacioWeb/Yazdani.pdf ) comparing with standard random walk in defected lattice and MERW ( …

Indeed in physics and our models we have asymptotically 1/r^{2} Coulomb force for topological/electric charges. For very low distances it is deformed - so called running coupling ( https://en.wikipedia.org/wiki/…constant#Running_coupling ) seen…

Higgs potential e.g. (|n|^{2} - 1)^2, quite popular in physics, here just means nontrivial vacuum - e.g. "director field" in liquid crystals, leading to electromagnetism as Goldstone bosons ... potential allows to deform to finite energy to prevent infinite…

Indeed electron being perfect point makes no sense - e.g. would have infinite energy of electric field, wouldn't have running coupling effect (as experiment and Faber have). Here are gathered experimental arguments for size of electron: …

Electric charge can be calculated through Gauss law by integrating electric field over closed surface - what has also topological analogue if interpreting spatial curvature of field as electric field. In similar way they experimentally get Coulomb-like…

I use topological charge as (2,3D) winding number for field restricted to a closed surface - it gives function from the surface to sphere, which has to cover this sphere an integer number of times. Such 2D topological charge is e.g. (integer) number of…