Electromagnetism with built-in electric charge quantization as topological

I will discuss topological solitons starting with 1+1 dimensional sine-Gordon model. Then I will consider higher dimensional model, like topological defects with long-range e.g. Coulomb-like interactions observed in liquid crystals. To recreate electromagnetism for them (Faber's approach), we use standard EM Lagrangian for dual electromagnetic tensor F defined as curvature of some deeper field of e.g. unitary vectors. In this way the Gauss law counts topological charge of this deeper field, getting the missing charge quantization. To regularize the central singularity to finite energy, we use a Higgs-like potential. I will also discuss some extensions to other particles.

The presentation is available at: https://www.dropbox.com/s/aj6tu93n04rcgra/soliton.pdf