Has the Charge Quantization Problem Been Solved Without Magnetic Monopoles?

In summary, the author claims to have found a way to explain charge quantization without the need for magnetic monopoles, using an analogy between bundles and the electromagnetic field. He is using complex line bundles instead of principal U(1)-bundles, and he uses omega to be the curvature of the connection, but d(omega)=*(alpha), and not zero.
  • #1
vonZarovich
2
0
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).
 
  • #3
I would also appreciate an insight from the more mathematical knowledgeable guys of the forum.
 
  • #4
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.
 

1. What is the charge quantization problem?

The charge quantization problem refers to the observation that electric charge, which is a fundamental property of matter, is always found in discrete, quantized amounts. This means that the smallest unit of charge, known as the elementary charge, is never observed to be in fractions or multiples of itself.

2. How was the charge quantization problem solved?

The charge quantization problem was solved through the experiments conducted by Robert Millikan in 1909, where he measured the charge of an electron to be a discrete value of 1.602 x 10^-19 coulombs. This discovery provided evidence for the existence of quantized charge and helped to establish the field of quantum mechanics.

3. Why is charge quantization important?

Charge quantization is important because it helps to explain the fundamental structure of matter and how it interacts with electromagnetic forces. It also plays a crucial role in the development of modern technologies, such as electronics and telecommunications.

4. Are there any exceptions to charge quantization?

While the charge of individual particles is always quantized, there are some phenomena in the quantum world that can exhibit continuous charge values, such as quarks and gluons. However, these particles are always confined within larger particles, making the overall charge of the system quantized.

5. How does charge quantization relate to the conservation of charge?

Charge quantization is closely related to the conservation of charge, which is a fundamental law in physics stating that the total electric charge in a closed system must remain constant. The quantized nature of charge ensures that this conservation law is always upheld, as the charge cannot be created or destroyed in discrete amounts.

Similar threads

No explanation of quantized charge from U(1)?
    • High Energy, Nuclear, Particle Physics
Replies
9
Views
7K
Field Energy of Permanent Magnets vs. Magnetic Monopoles
    • Electromagnetism
Replies
27
Views
3K
A On the relationship between Chern number and zeros of a section
    • Differential Geometry
Replies
3
Views
2K
B Preon quark models excluded by LHC
    • Beyond the Standard Models
Replies
7
Views
2K
I How powerful would a collider have to be to observe a sphaleron?
    • High Energy, Nuclear, Particle Physics
Replies
2
Views
2K
A Three generations of Fermions from octonions Clifford alegbras
    • Beyond the Standard Models
2
Replies
61
Views
6K
Can magnetic field exist without electric field?
    • Electromagnetism
2
Replies
38
Views
28K
A Susceptibilites for the Anderson Impurity Model
    • Atomic and Condensed Matter
Replies
1
Views
1K
I Trying To Conceptualize Two Dimensions Of Time
    • Beyond the Standard Models
Replies
2
Views
2K
Dirac's magnetic charge generalization of maxwell's equations?
    • Electromagnetism
Replies
2
Views
3K

Hot Threads

Recent Insights

Back
Top