Jarek wrote:Higgs-like potential as above regularizes charges to finite energy without any artificial cutoffs (also leading to charge quantization due to minimum having nontrivial topology) - as in diagram above: electromagnetism deforms into other interactions in particles to prevent infinities.
I believe the following is the complete QED Lagrangian for a free charged fermion or close to it that includes gravitational torsion.
Where .
The second term on the RHS is the charge interacting with the field it creates. The last term on the RHS is the torsion term and it is basically the intrinsic spin interacting with itself and has the gravitational coupling but that can be shown related to Planck length. There is no external potential necessary like in Faber's soliton model. The Lagrangian can be solved for length factors for a static situation and two positive solutions are obtained. One near the classical radius and one near Planck length. Of course the one near the classical radius has been excluded by experiment but Compton wavelength can be extracted from it. So we can see that including gravitational torsion provides a natural cutoff and no external potential is necessary.
However..., one still wonders how this can be kept together as a particle. So I am wondering if there might be a soliton solution for the above Lagrangian?
.