Questions tagged [magnetic-monopoles]

A magnetic monopole is a hypothetical particle with only one magnetic pole. Their magnetic fields would not be divergence-less. Predicted by certain modern theories, including string theory, supergravity, and various popular grand unified theories.

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Is it possible to introduce magnetic monopoles without breaking $∇ · B = 0$?

In another word, the net magnetic charge is always zero everywhere, which means magnetic field is still strictly source free. On the other hand, the net magnetic current jm can be nonzero, which means ...
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Maximum $B$-field at the surface of a permanent magnet

I have the dipole formula for a permanent spherical magnet in coordinate-free form. $\vec{B}=\frac{\mu_{0}}{4\pi}\frac{3(\vec{m}\cdot\hat{r})\hat{r}-\vec{m}}{r^{3}}$ I am trying to find the maximum $B$...
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Why are magnetic monopoles "incompatible" with quantum mechanics?

I'm reading this Physics Today article on magnetic monopoles, and I'm a bit confused by a discussion of the necessity of Dirac strings for compatibility with quantum mechanics. I'll reproduce the ...
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On rotating magnetic charges

Consider a sphere with magnetic charge $P$ and electric charge $Q$. We know that when the sphere is subjected to rotation about the $z$-axis, there is a magnetic dipole moment generated from the ...
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Is charge not quantized fundamentally and that is why we haven't come across magnetic monopole?

If protons are getting charged from quarks.. then the charge in quarks is fractional and not quantized. Does this mean that the charge we see is not fundamental? And the charges in quarks are just ...
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Can cosmological defects escape a black hole?

Based on my understanding, anything that can't move faster than light can't get out of a black hole, but space can since it can move faster than light (hence cosmic inflation is exponentiated). Also, ...
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Magnetic field with periodic boundary conditions, torus and magnetic monopoles

Suppose I have a 2D square lattice in the xy-plane, and I apply a uniform magnetic field in the z-direction. To simplify calculations, I would like to assume periodic boundary conditions in both the x ...
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Berry flux of magnetic monopole

I am sorry if it looks stupid question. I want to ask how sin is transferred back from spherical to Cartesian and how $F_{ij}$ tells us about magnetic monopole in magnetic field. $F_{ij}$ is berry ...
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Why would magnetic monopoles not violate the law of conservation of energy?

The field lines around a magnetic dipole are continuous unending loops. If magnetic monopoles were to exist, we could limit the path of a monopole along one of these field lines where it will continue ...
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Have magnetic monopoles been predicted to have been produced in other cases than those of symmetry breaking in GUTs?

Also, what other configurations are magnetic monopoles theorized to exist in? (such as black holes, monopole walls etc.)
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How can holographic duals (eg. AdS/CFT) be used to study magnetic monopoles? [closed]

What useful things are possible to find out about magnetic monopoles through the use of dual theories? I'm thinking of characteristics such as stability (or chaoticness), expectation values, central ...
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Possible charge for Abelian and non-Abelian theory

I am reading Tong's lecture note gauge theory. On page 6 in chapter 1 he writes Instead, the key distinction is the choice of Abelian gauge group. A $U(1)$ gauge group has only integer electric ...
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Suppose an isolated north pole exists. Then would it surely move along magnetic field line of a bar magnet as written in my book?

My book says that magnetic field lines due to a bar magnet are the path along which a unit north pole would move (if it existed). Will it surely move along the field line? I mean the two poles of ...
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Is an electron a topological defect? [duplicate]

Magnetic monopoles such as the t'Hooft Polyakov monopoles are special field configurations within some SU(2) gauge theory, that are characterised by their non trivial topology, thus calling them one ...
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How to derive Dirac's quantization of electric and magnetic charge from Berry's phase?

I have seen two ways of deriving Dirac's quantization of electric and magnetic charge using Berry's phase, one from Sakurai's book Modern Quantum Mechanics P354~355 and the other from David Tong's ...
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Cosmic strings, domain walls, and magnetic monopoles are topological defects, but what's defecting?

Wikipedia gives an explanation of cosmic strings that I'm sure would be very helpful if I had a major in topology, but alas I do not. I know that a topological defect is any sort of discontinuity in a ...
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Why monopoles of magnets do not exist? [duplicate]

Why monopoles (in magnets) do not exist?
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What particles are thought to have existed before Inflation?

What fundamental particles do most Grand Unified and Inflationary theories predict existed before the Inflationary period? Basically, what do we expect the family of particles existing during the ...
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Are current loop and magnets 100% equivalent?

let's consider this picture taken from Wikipedia, It is written that: A magnetic dipole is the limit of either a closed loop of electric current or a pair of poles as the size of the source is ...
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Why does the extended Lorentz force law have a negative sign?

I read on a textbook (and Wikipedia) that, if there were magnetic charges, the theoretical corresponding Lorentz force law would be $$ \mathbf F = q_m\left( \mathbf B - \frac1{c^2}\mathbf v \times \...
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What does a monopole field "look like"?

If magnetic monopoles exist, they are predicted to have large charges--or equivalently, a large coupling constant, which means that perturbative models don't converge. While I get that that makes it ...
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What would happen if the fine structure constant were set to 1?

While reading up on magnetic monopoles, I have been led to understand that, due to S-duality, the magnetic equivalent of the fine-structure constant, $\alpha_M$ must be related to the reciprocal of $\...
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$AdS_2/CFT_1$ toy model of a magnetic monopole

Is it possible to create a holographic $AdS_2/CFT_1$ (2D/1D) toy model, which contains a magnetic monopole solution in the bulk? I would like to study certain behaviours on the boundary of a toy model ...
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If magnetic monopoles existed, would the electric field also require a vector potential? [duplicate]

I'm studying magnetic duality and it seems that duality is nearly complete for the exception of the apparent non-existence of magnetic monopoles. My issue here isn't this one. My issue is that, if ...
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Magnetic Charge through conducting loop

There's a problem in Griffith's book that I don't understand his solution : Here's the solution : What's the justification for $\varepsilon = -L\frac{\mathrm{d} I}{\mathrm{d} t}$ ? $$$$ This ...
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Where do magnetic monopoles get their magnetic fields from?

As I understand it, magnetism isn't a "real" force like electricity is – when you apply relativity to a moving charge, it produces an effect that can be described using magnetic fields, but ...
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What's the mathematical explanation of the emergence of magnetic monopoles during the early universe?

I would "simply" like to know the full mathematical explanation of: Why do these topological defects occur in the first place? And more importantly, Why must these defects/particles carry ...
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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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How do we perform a perturbative expansion for magnetic monopoles?

Magnetic monopoles in non-abelian (and even abelian) gauge theory essentially appear as a non-perturbative, composite phenomenon if we perform the standard perturbative expansion in terms of, say, ...
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Magnetic monopoles in an $SU(2)$ gauge theory

I had heard from a professor saying that "Polyakov and ’tHooft discover the magnetic monopoles in $SU(2)$ gauge theory with scalar fields [Georgi-Glashow model]." And he cited two references:...
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Magnetic charge model

If we use want to calculate the magnetic charges of a bar magnet to calculate the Force between 2 magnets can we calculate them from the strength of the magnetic field of the magnet(B) and if yes how? ...
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Magnetic monopoles in 2D

Question: Is it possible to have a gapless theory of 2+1 dimensional electromagnetism with magnetic monopoles but no electric monopoles? If such a theory exists, does a Lagrangian description exist? ...
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Does the existence of the monopole in a 2+1D $U(1)$ gauge theory require the gauge field compact?

I find the monopole is allowed in a 2+1D compact $U(1)$ gauge theory in lattice (Hermele, PRB 69,064404 (2004)), there the gauge field $A$ is also compact and takes value in $[0,2\pi)$, so there is a ...
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Galilean transformation of magnetic and electric field with magnetic monopole

Starting from the lorentz force in presence of a magnetic charge: $$\vec{F} = q_e(\vec E+\vec v\times \vec B)+q_m(\vec B - \vec v\times\vec E)\tag 1$$ by galilean invariance, we should have $\vec F =...
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Distinctness of magnetic monopoles from electric monopoles [closed]

If magnetic monopoles could exist, how would they differ from electric charges?
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If magnetic monopoles exist would magnetic charge contribute to weak hypercharge similar to how electric charge does?

Electromagnetism and the weak force are intertwined as two parts of the electroweak force and some links still exist even at low energy levels one of the being weak hypercharge which is determined by ...
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Bogomol'nyi-Prasad-Sommerfield (BPS) limit

When discussing the 't Hooft-Polyakov monopole and establishing the BPS bound, one also discusses BPS states and Bogomol'nyi-Prasad-Sommerfield limit. This limit sets $\lambda \to 0$ in the potential $...
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Magnetic charge of 't Hooft-Polyakov monopole

In "Quantum Field Theory", Srednicki defines the magnetic field in $SU(2)$ gauge theory as $$B^i= \epsilon^{ijk}\partial_j\left(\hat{\varphi}^a A_k^a \right)-\dfrac{1}{2e} \varepsilon^{ijk} \...
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How would a magnetically charged particle behave in matter?

Magnetically charged particles, or "magnetic monopoles", are a type of hypothetical elementary particle that may exist, though likely are very rare and/or hard to generate if they do. As the ...
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Why is magnetic ’t Hooft loop operator independent of its path in$Z_2$ gauge theory?

One important concept for $Z_2$ gauge theory is magnetic ’t Hooft loop operator $\tilde{W}_{\tilde{\Gamma}}$ along a non-contractible loop $\tilde{\Gamma}$ on the dual lattice of the torus is: $$\...
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Does the presence of magnetic monopole break the time reversal, or does its magnetic charge flip (more naturally)?

It is often said that the presence of magnetic field breaks the time reversal symmetry (see Sakurai quantum mechanics book p.285), because the Lorentz force law shows $$ \vec F = q(\vec E + \vec v \...
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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 ...
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Force law from Lagrangian for magnetic monopole

How to construct a Lagrangian that gives the Lorentz force law with both magnetic and electric monopole? I got that the force will be of the form \begin{equation} m \frac{\mathrm{d}x^\nu}{\mathrm{d}\...
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Magnetic monopole Lagrangian and Hamiltonian

How do I find an equation analogous to \begin{equation} \mathcal{L}(q,\dot q)=\frac12 m \dot q ^2-q\phi+q\vec{\dot q}\cdot \vec A\quad\quad \text{where}\quad \vec B =\vec\nabla\times\vec A, \quad \vec ...
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Electric and magnetic charge quantization v.s. the radius of the $U(1)$ or $\mathbb{R}$ gauge parameter

We know (say from Griffiths E&M Problem 8.12) that the electric $q_e$ and magnetic charge $q_m$ (with a distance $\vec{z}$ apart) can store the angular momentum in the space: $$ \vec{L}=\int d^3 V ...
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If we had access to magnetic monopoles, what types of “electromagnetronics” might that enable?

This is a very broad question, but answers that give any sort of insight are welcome. As we know, the electronics revolution of the 20th century was based on a variety of interesting electrodynamical ...
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Gilbert dipoles vs Ampere dipoles

In Griffiths' textbook there is this problem : His solution is that you can't tell whether it's Gilbert or Ampere because in the cavities the field would be the same but I don't understand why is ...
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2 answers
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Metric of spinning magnetically charged black hole

According to Wikipedia (as of 1/20/2021), black holes may be completely classified according to their mass, electric charge and angular momentum. Are there not also 'magnetic monopole' solutions to ...
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Magnetic monopole, vector-potential and differential forms

When written in the language of exterior algebra, Maxwell-Thomson equation writes as $dB=0$ where $d$ is the exterior derivative and $B$ is the magnetic flux 2-form. From Poincaré's lemma, it follows ...
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Vector potential field for a hypothetical magnetic monopole

This is a mathemetical question with perhaps a physical interpretation. I would like to solve the equation: $$ \vec{\nabla} \times \vec{A} = \frac{1}{r^2} \hat{r} \tag{1}$$ using spherical ...
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