Has the Charge Quantization Problem Been Solved Without Magnetic Monopoles?

[vonZarovich]

I am no mathematician, not even an expert in Gauge Theories, but I came across this article

http://arxiv.org/abs/1409.6716
(published here http://www.sciencedirect.com/science/article/pii/S0393044015002284)

when I was looking for some "condensed-matter-type-monopoles", and the author claims to have found a way to explain why electric charges are quantized without the need to magnetic monopoles.

As far as I understood the author uses an analogy between bundles and the electromagnetic field, which seems quite similar to the U(1) gauge formulation of electromagnetism, but he uses sort of high level mathematics (taking into account my own level on the subject) preventing me to tell if his theory explains charge quantization.

Can someone tell me if this is a solution to the problem?

I would also appreciate if someone could explain what he is doing using lower level mathematics, so I can actually follow (I am a graduate physics student working with applications of QFT in condensed matter).

 

[andresB]

I would also appreciate an insight from the more mathematical knowledgeable guys of the forum.

 

[vonZarovich]

I'm afraid that I'm still lost, Greg. I didn't dedicate a lot of time on this because I'm just curious, this is not related to the things I'm studying.

I've got a copy of Wald's book, and I was able to follow his section 2 (not the bit about the Lorentz force, though). Apart from some minus signs, my guess is that he isn't using the tensor F as everyone else, but he's using the dual tensor *F to be his differential form omega.

As I think I'm getting to understand, I realize that he doesn't even mention the word gauge in his text or potentials. He also uses complex line bundles instead of principal U(1)-bundles, but I've seen people using both for EM fields.

The common idea is to use dF=0 to give dA=F, where the potential A is going to be U(1)-connection. And the other equation is d*F=4pi*j. He is using omega to be the curvature of the connection, but d(omega)=*(alpha), and not zero...

His approach to topological charges in section 3 reminded me the whole business of instantons, but I though that Abelian theories had no such a thing.