137 views

### Why Dirac monopole is a topological defect in a $U(1)$ gauge theory? [duplicate]

How does $U(1)$ gauge group at long distances, give rise to magnetic monopoles? Also why is it said that Dirac monopole is a topological defect in a compact $U(1)$ gauge theory?
2k views

### Is there a topological difference between an electric monopole and an magnetic monopole?

When we introduce magnetic monopoles, we have duality, i.e. invariance under the exchange of electric and magnetic fields. Magnetic (Dirac) monopoles are usually discussed using topological ...
1k views

### What defines a large gauge transformation, really?

Usually, one defines large gauge transformations as those elements of $SU(2)$ that can't be smoothly transformed to the identity transformation. The group $SU(2)$ is simply connected and thus I'm ...
519 views

### Magnetic monopoles in field theory

In standard QED, we couple the electron to electromagnetism by replacing $$\partial_\mu \to \partial_\mu + i e A_\mu.$$ Upon taking the classical limit, we find that this gives electrons an electric ...
599 views

### Why magnetic monopole has't been shown in the particle physics's Standard Model context?

For various reasons, experts, since Dirac, believe that a unified field theory must have a magnetic monopole. For example, Polyakov said: "I am quite certain that magnetic monopoles really exist. How, ...
269 views

### Poincaré' lemma and EM potential $A^{\mu}$

My lecturer said that given the sourceless Maxwell's equations $$\partial_{\mu}\, ^ *F^{\mu\nu} = 0$$, we can find a solution $$F^{\mu\nu} = \partial_{\mu}A_{\nu} - \partial_{\nu}A_{\mu},$$ that ...
106 views

### Some questions about gauge theory

Let's talk quantum mechanics. I have a charged particle moving on a sphere. It has a wave function $\psi$. At time $t=0$, there is no magnetic flux piercing the sphere. Instantaneously, I introduce a ...
123 views

### Help understanding Dirac's argument for magnetic monopoles

I'm trying to understand Dirac's argument for monopoles in his 1931 paper$^1$, but for me it's still a tough read (undergrad physicist). I can begin to summarize his argument as follows: Take a very ...