Questions tagged [dirac-monopole]

29 questions
21
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3 answers

Are the recently observed Dirac monopoles separable?

I just went through Observation of Dirac monopoles in a synthetic magnetic field. What exactly has been observed? More importantly, are these monopoles localized inside the apparatus (no stray monopole field lines coming out), or can they be used to…
14
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1 answer

Is a magnetic monopole really necessary for charge quantization?

The usual remark that goes about in a first encounter of Dirac monopoles is that it solves the problem of electric charge quantization. I have also studied t'Hooft Polyakov monopoles which asymptotically quantize the charge. Basically they prove…
13
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2 answers

Why do we like gauge potentials so much?

Today I read articles and texts about Dirac monopoles and I have been wondering about the insistence on gauge potentials. Why do they seem (or why are they) so important to create a theory about magnetic monopoles? And more generally, why do we like…
9
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2 answers

First Chern number, monopoles and quantum Hall states

The first Chern number $\cal C$ is known to be related to various physical objects. Gauge fields are known as connections of some principle bundles. In particular, principle $U(1)$ bundle is said to be classified by first Chern number. In terms of…
9
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1 answer

Why isn't Dirac credited with the discovery of the Aharonov-Bohm effect?

Above equation (8) of Dirac's famous 1931 paper in which he proposes his quantization condition for magnetic monopoles, he says "the change in [an electron's] phase around [a] closed curve [is] $2 \pi n + e/\hbar c \int {\bf H} \cdot d{\bf S}$." …
8
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1 answer

What do we mean when we say the QM wave function is a section of the $U(1)$ bundle?

I have a couple questions here. To keep the discussion simple lets stick to the following case: what is the quantum mechanics of a single particle in the presence of a background EM field, such as that of a monopole, where multiple coordinate…
8
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1 answer

Question about Monopole Operator

I've been studying IR-dualities in 2+1 dimensions. I encountered monopole operators in the following paper: Time-Reversal Symmetry, Anomalies, and Dualities in (2+1)d On page 10, starting from $QED_{3}$ with $N_{f}$ fermions of charge 1, the…
8
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2 answers

What was Dirac's motivation to study hypothetical magnetic monopoles?

The equation $$\boldsymbol{\nabla}\cdot\textbf{B}(\textbf{r})=0\tag{1} $$ dictates that there can be no isolated magetic monopole. What was then the motivation for Dirac to consider the consequences for a hypothetical magnetic monopole? Using…
8
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1 answer

This vector potential gives a magnetic monopole field, what's wrong with it?

$\mathbf{A} = \frac{g(1-\cos\theta)}{r\sin\theta} \mathbf{\hat\phi} \Rightarrow \mathbf{B} = g \mathbf{\hat r}/r^2$ But yet the existence of $\mathbf{A}$ itself hinges on the fact that there are no magnetic monopoles. Is the problem because the…
6
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2 answers

Magnetic monopoles in spin ice and Dirac string comparison

In spin ice systems magnetic monopole-like excitations are sources or sinks of $H$, not the $B$ field, why is that? Is it because the strings carries magnetic moment $M$ and not solenoidal $B$ filed like the Dirac string. How is it different from…
6
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2 answers

Why did David Tong say that the global topological $U(1)$ symmetry is unbroken in Higgs phase?

In the paper A Duality Web in 2+1 Dimensions and Condensed Matter Physics by Seiberg, Senthil, Wang, and Witten, they studied the particle-vortex dualities in $2+1$ dimensions. On page 20, section 3.1, they considered phase transitions of the $2+1$…
6
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1 answer

Dirac string and Nielsen–Ninomiya theorem

Nielsen–Ninomiya theorem states that in a lattice system one can not have just one chiral fermion. Fermions necessarily come in pairs of opposite chirality. I am wondering if one can "explain" this theorem using the following argument: Since a Weyl…
6
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1 answer

Distinction of Dirac monopole and Polyakov-'t Hooft monopole

Can anybody explain the physical difference between Dirac monopole and Polyakov monopole? First, let me write down what I know briefly. Dirac monopole It comes from the symmetry of Maxwell equation. By assuming that magnetic field for a point…
6
votes
1 answer

Quantum ring and Dirac Quanitzation

I had a small question. If you look at the energy eigenvalue problem for a particle restricted to a ring, you get $$E_n = \frac{\hbar^2n^2}{2mR^2}.$$ If you then put a solenoid inside the ring, then the values shift to $$E_n =…
user33525
5
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2 answers

Dirac magnetic monopoles and quark fractional electric charge quantization

When applying the Dirac quantization rule for electric and magnetic charge, I assume one is considering unit electric charges such as electrons. How does the Dirac quantization rule apply for the fractional electric charges of quarks?
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