Linked Questions

2
votes
0answers
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?
15
votes
5answers
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 ...
13
votes
1answer
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 ...
4
votes
1answer
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 ...
2
votes
2answers
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, ...
1
vote
1answer
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 ...
1
vote
1answer
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 ...
0
votes
0answers
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 ...
1
vote
0answers
92 views

Is the Dirac string continuous?

Is the Dirac string continuous? Suppose I have a point magnetic charge. Do the necessary singularities of the vector potential lie on a continuous curve in 3D space?
3
votes
0answers
75 views

Maxwell theory : How to justify the potential gauge fields if there are magnetic monopoles?

Without magnetic monopoles, the Maxwell equations are these (I'm dropping vector notations and all constants, for simplicity): \begin{align} \nabla \cdot E &= \rho_{elec}, \tag{1} \\[12pt] \nabla \...