Questions tagged [dirac-string]
17 questions
11
votes
4 answers
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 of charge.
Okay, it looks great. But is this the…
Isaac
- 2,986
9
votes
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] $2 \pi n + e/\hbar c \int {\bf H} \cdot d{\bf S}$." …
tparker
- 51,104
8
votes
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…
SRS
- 27,790
- 13
- 115
- 365
8
votes
1 answer
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 $e$ or $\frac{e}{3}$ because of the quarks'…
tparker
- 51,104
6
votes
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…
Sergej Moroz
- 591
6
votes
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…
phy_math
- 3,782
5
votes
1 answer
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 seen in Goddard and Olive's review)
But, for a…
Leandro Seixas
- 1,318
4
votes
1 answer
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 $\delta{(x_\mu)}$ is dirac delta.
So in many places (for…
physshyp
- 1,449
2
votes
0 answers
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 magnetic field is generated by the following…
Sonia Llambias
- 378
2
votes
0 answers
Are we sure that electric “monopoles” are not just ends of an “Electrical Dirac String”?
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 current of “magnetic charges”? Could an electrical…
Kevin Marinas
- 129
1
vote
3 answers
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 choice of ${\bf A}({\bf r})$, extending from the…
SRS
- 27,790
- 13
- 115
- 365
1
vote
0 answers
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 singularity at the positive $z$ axis like a Dirac…
Weicheng Ye
- 252
- 1
- 9
1
vote
1 answer
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 proportional to $\Theta(-z)\delta(x)\delta(y)$ on the $z$…
Chris I
- 13
1
vote
0 answers
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?
André Guerra
- 11
0
votes
0 answers
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 is the integration carried out in some limited…
skachko
- 91