Questions tagged [dirac-string]
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17 questions
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Dirac string and nature of singularities
The Dirac magnetic monopole is defined as
\begin{align}
\vec{B}=\frac{g\vec{r}}{r^3}\,,
\end{align}
where $g$ is the strength of the monopole and $\vec{r}$ a vector. It is possible to show that the ...
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Are we sure that electric “monopoles” are not just ends of an “Electrical Dirac String”? [closed]
The Dirac String is used to model magnetic monopoles. So how are we sure that physical electric “monopoles” are not in fact the ends of an “Electrical Dirac String” produced by a solenoid carrying a ...
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What definition of integral is implied when expressing nonzero Chern number as the integral of Berry curvature?
In defining a nonzero Chern number as the integral of Berry curvature over the parameter manifold: $$n=\frac{1}{2\pi}\int_{S}{\mathcal{F}}{dS}$$ does the integral exist in a general Riemann sense, or ...
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Is this case a failure of Stokes' theorem?
In the presence of a hypothetical magnetic point charge at the origin of coordinates, it turns out that an irremovable physical singularity of the vector potential ${\bf A}({\bf r})$ exists for any ...
- 27.2k
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Why curl of Dirac string attached to Dirac monopole is zero?
So let we have a magnetic field which is
$$B_\mu=\frac{q}{2}\frac{x_\mu}{|x|^3}-2\pi q\delta_{3\mu}\theta(x_3)\delta{(x_1)}\delta{(x_2)},\tag{4.65}$$
where $\theta$ is step function and $\delta{(x_\mu)...
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Does the electrodynamics-like PDE $\epsilon^{ijk}\partial_j B_{kl}(x) = \delta^i_l\delta^{(3)}(x)$ have solutions?
Consider the following PDE in 3 dimensions
$$ \epsilon^{ijk}\partial_j B_{kl}(x) = \delta^i_l\delta^{(3)}(x)$$
Does $B_{kl}(x)$ have a solution? (It can have any kind of singularity, e.g. it can have ...
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How to incorporate Dirac's magnetic monopole solution into a continuous magnetic charge density?
Dirac famously solved Maxwell equations in the presence of a point magnetic monopole. He was able to do so in a manner which used only the standard vector potential $\vec{A}$ and gave the correct ...
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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 ...
- 27.2k
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Singularity of $B$-field in a Dirac String
I was assigned this question related to Dirac strings:
Given a vector potential $\vec{A}= \frac{1-\cos(\theta)}{r\sin(\theta)}\hat{\phi}$, show that there is a singularity in the $B$ field ...
- 13
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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 ...
- 49.4k
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Which charge to use in the Dirac quantization condition?
I have a follow-up question to Dirac magnetic monopoles and quark fractional electric charge quantization, regarding whether the "unit of electric charge" in the Dirac quantization condition should be ...
- 49.4k
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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 ...
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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?
- 11
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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 ...
- 3,662
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Vector potential in presence of monopole [duplicate]
In this paper http://www.hcs.harvard.edu/~jus/0302/song.pdf when Song was explaining dirac string. He said "In the presence of a magnetic monopole, the vector potential cannot be defined everywhere. ...
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Can one introduce magnetic monopoles without Dirac strings?
To introduce magnetic monopoles in Maxwell equations, Dirac uses special strings, that are singularities in space, allowing potentials to be gauge potentials. A consequence of this is the quantization ...
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Dirac string on (periodic) compact space
For a non-compact space, the Dirac string can be defined as a line joining the Dirac monopole to infinity (or another Dirac monopole). The region where the gauge connection is ill-defined. (as can be ...
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