by Jarek » Sun Apr 19, 2020 9:58 am
Field has to be defined everywhere, including for radius down to zero.
One more time, regularization is thanks to potential, like Higgs' below: V(u) = (|u|^2-1)^2.
This potential makes that field prefers |u|=1 unitary vectors - minimum of potential refereed as vacuum, its dynamics leads to EM in Faber's model, quantzation is thanks to having nontrivial topology.
However, maintaining |u|=1 to the center of singularity (e.g. hedgehog), energy of this field would be infinite due to noncontinuity - to prevent that, field activates potential, getting to u=0 in the center of singularity, as in vector field below.
So in vacuum we have electromagnetism, which deforms into other interactions (weak/strong) inside particles to prevent infinity - by activating Higgs' potential (getting out of its minimum).
Observed experimental consequence of this finite size is running coupling - that Coulomb interaction is deformed for very small distances.
Field has to be defined everywhere, including for radius down to zero.
One more time, regularization is thanks to potential, like Higgs' below: V(u) = (|u|^2-1)^2.
This potential makes that field prefers |u|=1 unitary vectors - minimum of potential refereed as vacuum, its dynamics leads to EM in Faber's model, quantzation is thanks to having nontrivial topology.
However, maintaining |u|=1 to the center of singularity (e.g. hedgehog), energy of this field would be infinite due to noncontinuity - to prevent that, field activates potential, getting to u=0 in the center of singularity, as in vector field below.
So in vacuum we have electromagnetism, which deforms into other interactions (weak/strong) inside particles to prevent infinity - by activating Higgs' potential (getting out of its minimum).
Observed experimental consequence of this finite size is running coupling - that Coulomb interaction is deformed for very small distances.
[img]https://i.imgur.com/lCvYXwK.png[/img]