Magnetic monopole

Magnetic monopole
Magnetic monopole
Involved in interactions	Gravity , electromagnetic
Status	Hypothetical
In honor of whom or what is named	Nonzero magnetic charge - a point source of radial magnetic field
Quantum numbers

A magnetic monopole is a hypothetical elementary particle with a nonzero magnetic charge - a point source of a radial magnetic field . Magnetic charge is a source of static magnetic field in the same way as electric charge is a source of static electric field .

A magnetic monopole can be represented as a single pole of a long and thin permanent magnet . However, all known magnets always have two poles, that is, it is a dipole . If you cut the magnet into two parts, then each of its parts will still have two poles. All known elementary particles having an electromagnetic field are magnetic dipoles.

Content

History

With the creation of physics as a science based on experience, the opinion was firmly established that the electrical and magnetic properties of bodies differ significantly. This view was clearly expressed by William Hilbert in 1600 . The identity of the laws of attraction and repulsion established by Charles Coulomb for electric charges and magnetic charges - the poles of magnets again raised the question of the similarity of electric and magnetic forces, but by the end of the XVIII century it was found out that in laboratory conditions it is impossible to create a body with a nonzero total magnetic charge. The concept of “magnetically charged substance” was expelled from physics for a long time after the work of Ampere in 1820 , in which it was proved that the circuit with an electric current creates the same magnetic field as a magnetic dipole.

In 1894, Pierre Curie stated in a short note that the introduction of magnetic charges into Maxwell's equations is natural and only makes them more symmetrical.

Symmetry of Maxwell's equations

The equations of classical electrodynamics formulated by Maxwell relate the electric and magnetic fields to the motion of charged particles. These equations are almost symmetrical with respect to electricity and magnetism. They can be made completely symmetrical if, in addition to the electric charge $q_{\mathrm {e} }$ ${\ displaystyle q _ {\ mathrm {e}}}$ and introduce a certain magnetic charge to the current $q_{\mathrm {m} }$ ${\ displaystyle q _ {\ mathrm {m}}}$ (magnetic charge density $\rho _{\mathrm {m} }$ ${\ displaystyle \ rho _ {\ mathrm {m}}}$ ) and magnetic current (magnetic current density $\mathbf {j} _{\mathrm {m} }$ ${\ displaystyle \ mathbf {j} _ {\ mathrm {m}}}$ ):

Maxwell's equations and the Lorentz force with magnetic monopoles: SI units
Title	Without magnetic monopoles	With magnetic monopoles (Weber Convention)	With magnetic monopoles (ampere convention)
Gauss theorem :	$\nabla \cdot \mathbf {E} ={\frac {\rho _{\mathrm {e} }}{\varepsilon _{0}}}$ ${\ displaystyle \ nabla \ cdot \ mathbf {E} = {\ frac {\ rho _ {\ mathrm {e}}} {\ varepsilon _ {0}}}}$
Gaussian Magnetic Law	$\nabla \cdot \mathbf {B} =0$ ${\ displaystyle \ nabla \ cdot \ mathbf {B} = 0}$	$\nabla \cdot \mathbf {B} =\rho _{\mathrm {m} }$ ${\ displaystyle \ nabla \ cdot \ mathbf {B} = \ rho _ {\ mathrm {m}}}$	$\nabla \cdot \mathbf {B} =\mu _{0}\rho _{\mathrm {m} }$ ${\ displaystyle \ nabla \ cdot \ mathbf {B} = \ mu _ {0} \ rho _ {\ mathrm {m}}}$
Faraday's law of induction :	$\nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}$ ${\ displaystyle \ nabla \ times \ mathbf {E} = - {\ frac {\ partial \ mathbf {B}} {\ partial t}}}$	$\nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}-\mathbf {j} _{\mathrm {m} }$ ${\ displaystyle \ nabla \ times \ mathbf {E} = - {\ frac {\ partial \ mathbf {B}} {\ partial t}} - \ mathbf {j} _ {\ mathrm {m}}}$	$\nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}-\mu _{0}\mathbf {j} _{\mathrm {m} }$ ${\ displaystyle \ nabla \ times \ mathbf {E} = - {\ frac {\ partial \ mathbf {B}} {\ partial t}} - \ mu _ {0} \ mathbf {j} _ {\ mathrm {m }}}$
Ampere Law (with bias current ):	$\nabla \times \mathbf {B} ={\frac {1}{c^{2}}}{\frac {\partial \mathbf {E} }{\partial t}}+\mu _{0}\mathbf {j} _{\mathrm {e} }$ ${\ displaystyle \ nabla \ times \ mathbf {B} = {\ frac {1} {c ^ {2}}} {\ frac {\ partial \ mathbf {E}} {\ partial t}} + \ mu _ { 0} \ mathbf {j} _ {\ mathrm {e}}}$
The power of Lorentz	$\mathbf {F} =q_{\mathrm {e} }\left(\mathbf {E} +\mathbf {v} \times \mathbf {B} \right)$ ${\ displaystyle \ mathbf {F} = q _ {\ mathrm {e}} \ left (\ mathbf {E} + \ mathbf {v} \ times \ mathbf {B} \ right)}$	$\mathbf {F} =q_{\mathrm {e} }\left(\mathbf {E} +\mathbf {v} \times \mathbf {B} \right)$ ${\ displaystyle \ mathbf {F} = q _ {\ mathrm {e}} \ left (\ mathbf {E} + \ mathbf {v} \ times \ mathbf {B} \ right)}$ $+{\frac {q_{\mathrm {m} }}{\mu _{0}}}\left(\mathbf {B} -\mathbf {v} \times {\frac {\mathbf {E} }{c^{2}}}\right)$ ${\ displaystyle + {\ frac {q _ {\ mathrm {m}}} {\ mu _ {0}}} \ left (\ mathbf {B} - \ mathbf {v} \ times {\ frac {\ mathbf {E }} {c ^ {2}}} \ right)}$	$\mathbf {F} =q_{\mathrm {e} }\left(\mathbf {E} +\mathbf {v} \times \mathbf {B} \right)$ ${\ displaystyle \ mathbf {F} = q _ {\ mathrm {e}} \ left (\ mathbf {E} + \ mathbf {v} \ times \ mathbf {B} \ right)}$ $+q_{\mathrm {m} }\left(\mathbf {B} -\mathbf {v} \times {\frac {\mathbf {E} }{c^{2}}}\right)$ ${\ displaystyle + q _ {\ mathrm {m}} \ left (\ mathbf {B} - \ mathbf {v} \ times {\ frac {\ mathbf {E}} {c ^ {2}}} \ right)}$

In this case, the modified equations with magnetic monopoles pass into the classical equations when substituting $\rho _{\mathrm {m} }=0$ ${\ displaystyle \ rho _ {\ mathrm {m}} = 0}$ and $\mathbf {j} _{\mathrm {m} }=0$ ${\ displaystyle \ mathbf {j} _ {\ mathrm {m}} = 0}$ that is, if there are no magnetic charges in the considered region of space. Thus, it is possible to create a system of Maxwell equations taking into account the existence of magnetic charges, while the classical equations simply reflect the fact that usually magnetic charges are not observed.

If magnetic charges exist, then the existence of magnetic currents will lead to significant corrections of the Maxwell equations , which can be observed at macroscopic scales.

In the new form of Maxwell's equations, difficulties arise in the mathematical description using the vector potential. In the presence of both magnetic and electric charges, the electromagnetic field cannot be described using the vector potential $\mathbf {A} _{\mu }$ ${\ displaystyle \ mathbf {A} _ {\ mu}}$ $(\mu =0,\;1,\;2,\;3)$ ${\ displaystyle (\ mu = 0, \; 1, \; 2, \; 3)}$ continuous throughout the space. Therefore, in the presence of magnetic charges, the equations of motion of charged particles are not derived from the variational principle of least action . In classical electrodynamics, this does not lead to fundamental difficulties (although it makes the theory somewhat less beautiful), but quantum dynamics cannot be formulated outside the framework of the Hamiltonian or Lagrangian formalism.

Dirac Monopoly

Paul Dirac suggested the existence of a particle with a magnetic charge and came to the nontrivial conclusion that the magnetic charge of the proposed monopole cannot have an arbitrary value, but must be equal to an integer multiple of a certain amount of magnetism. ^[2]

The problem of determining the vector potential $A$ ${\ displaystyle A}$ giving a magnetic field $H$ ${\ displaystyle H}$ is mathematically equivalent to the problem of determining the current system $j^{'}$ ${\ displaystyle j '}$ creating a magnetic field $H^{'}$ ${\ displaystyle H '}$ . A constant current with uniform density in all directions should flow from a point emitting a constant magnetic field flux. To maintain it, it is necessary to supply a current to this point along a conducting thread, equal to the current emanating from this point in all directions, and the strength of this current is equal to the magnetic charge $g$ ${\ displaystyle g}$ . ^[3] Since the location of such a filament is completely arbitrary, the difference in vector potentials is equal to the magnetic field created by the current flowing to the point along one filament and flowing along the other filament. Such a magnetic field can be represented in the form of a multi-valued potential, the value of which at each point in space changes with each round of the loop associated with the thread, by the magnitude of the current multiplied by $4\pi$ ${\ displaystyle 4 \ pi}$ . From quantum mechanics it is known that the wave function $\psi$ ${\ displaystyle \ psi}$ characterizing a particle with a charge $e$ ${\ displaystyle e}$ when it changes $A\rightarrow A+\operatorname {grad} f$ ${\ displaystyle A \ rightarrow A + \ operatorname {grad} f}$ as $\psi \rightarrow \psi \exp \left({\frac {ie}{\hbar c}}f\right)$ ${\ displaystyle \ psi \ rightarrow \ psi \ exp \ left ({\ frac {ie} {\ hbar c}} f \ right)}$ . When looping around $f=4\pi g$ ${\ displaystyle f = 4 \ pi g}$ . But when going around the contour, the wave function should not change, therefore $\exp \left({\frac {ie}{\hbar c}}4\pi g\right)=1$ ${\ displaystyle \ exp \ left ({\ frac {ie} {\ hbar c}} 4 \ pi g \ right) = 1}$ . A complex number is one if it is represented as $\exp(2\pi in)$ ${\ displaystyle \ exp (2 \ pi in)}$ where $n$ ${\ displaystyle n}$ Is an arbitrary integer. Therefore: ${\frac {ie}{\hbar c}}4\pi g=2\pi in$ ${\ displaystyle {\ frac {ie} {\ hbar c}} 4 \ pi g = 2 \ pi in}$ where $n$ ${\ displaystyle n}$ Is an integer. Thus magnetic charge $g$ ${\ displaystyle g}$ particles must be a multiple of the elementary magnetic charge $g_{0}={\frac {\hbar c}{2e}}$ ${\ displaystyle g_ {0} = {\ frac {\ hbar c} {2e}}}$ where $e$ ${\ displaystyle e}$ - elementary electric charge . ^[four]

The converse is noteworthy: the existence of a magnetic charge does not contradict standard quantum mechanics only if the electric charges of all particles are quantized. (Thus, the existence in nature of at least one magnetic monopole with a certain charge would explain the experimentally observed multiplicity of electric charges of particles to $e$ ${\ displaystyle e}$ ; in this case, the magnetic charge would also need to be quantized.)

The Dirac quantization condition is generalized to the interaction of two particles, each of which has both an electric and a magnetic charge (such particles are called dions )

{\frac {e_{1}g_{2}-e_{2}g_{1}}{2\pi \hbar c}}=n.

{\ displaystyle {\ frac {e_ {1} g_ {2} -e_ {2} g_ {1}} {2 \ pi \ hbar c}} = n.}

(In the used system of units $e$ ${\ displaystyle e}$ and $g$ ${\ displaystyle g}$ have the same dimension, and the charge $e$ ${\ displaystyle e}$ fixed by the relation $e^{2}/4\pi \hbar c=1/137$ ${\ displaystyle e ^ {2} / 4 \ pi \ hbar c = 1/137}$ .)

In the nonrelativistic approximation, the force acting on dion 1 with coordinates $r$ ${\ displaystyle r}$ and speed $v$ ${\ displaystyle v}$ from the side of dion 2, fixed at the origin, is

F={\frac {(e_{1}e_{2}+g_{1}g_{2})\mathbf {r} +(e_{1}g_{2}-e_{2}g_{1}){\dfrac {[\mathbf {vr} ]}{c}}}{4\pi r^{3}}}.

{\ displaystyle F = {\ frac {(e_ {1} e_ {2} + g_ {1} g_ {2}) \ mathbf {r} + (e_ {1} g_ {2} -e_ {2} g_ { 1}) {\ dfrac {[\ mathbf {vr}]} {c}}} {4 \ pi r ^ {3}}}.}

Note that the combinations of charges included in this formula are invariant under the dual transformation .

'T Hooft-Polyakov Model

In 1974, A. M. Polyakov and Gerard 't Hooft (G.' t Hooft) independently discovered ^[5] that the existence of a magnetic monopole is not only possible, but also necessary in field theories of a certain class. In grand unification models that consider symmetry with respect to phase transformations of the wave functions of charged particles as an integral part of wider non-Abelian gauge symmetry, the electromagnetic field is associated with a multiplet of charged gauge fields $X$ ${\ displaystyle X}$ with large masses (these masses arise with spontaneous symmetry breaking). For some gauge symmetry groups, stable field configurations exist $X$ ${\ displaystyle X}$ localized in an area of size $l<\hbar /M_{X}c$ ${\ displaystyle l <\ hbar / M_ {X} c}$ and creating a spherically symmetric magnetic field outside this region. The existence of such configurations depends on the topological properties of the gauge group, more precisely, on how the subgroup of symmetry that has survived after spontaneous breaking is embedded in it. The stability of these magnetic monopoles is determined by the special behavior of the fields at large distances from the center. The mass of the magnetic monopole $M_{m}$ ${\ displaystyle M_ {m}}$ can be calculated, it depends on the specific field model, but in any case it should be large, $M_{m}\gg M_{X}$ ${\ displaystyle M_ {m} \ gg M_ {X}}$ (estimated for a wide class of models $M_{m}\sim 10^{16}{\frac {GeV}{c^{2}}}$ ${\ displaystyle M_ {m} \ sim 10 ^ {16} {\ frac {GeV} {c ^ {2}}}}$ ) These magnetic monopoles could be born in a hot Universe shortly after the Big Bang during a phase transition associated with spontaneous symmetry breaking and the appearance of non-zero uniform scalar fields in a vacuum. The number of magnetic monopoles being born is determined by the process of the development of the Universe at an early stage, therefore, by their absence, one can now judge this process. One explanation for the fact that relic magnetic monopoles are not detected is given by the theory of a swelling Universe (inflation). 'T Hooft - Polyakov magnetic monopoles have some unusual properties that make them easy to spot. In particular, interaction with a magnetic monopole can stimulate nucleon decay, predicted by some grand unification models ^[6] , that is, act as a catalyst for such a decay.

Basic physical properties

Magnetic Monopole Charge

The dimension of the charge of the magnetic monopole coincides with the dimension of the electric charge in the GHS system:

g_{D}={\frac {c\hbar }{2e}}={\frac {e}{2\alpha _{E}}}\approx 137e/2,\

{\ displaystyle g_ {D} = {\ frac {c \ hbar} {2e}} = {\ frac {e} {2 \ alpha _ {E}}} \ approx 137e / 2, \}

Where $c$ ${\ displaystyle c}$ Is the speed of light in vacuum, $\hbar$ ${\ displaystyle \ hbar}$ - Planck's constant and $e$ ${\ displaystyle e}$ - elementary charge .

In the SI system , the dimensions of magnetic and electric charges are different (Weber convention):

g_{D}={\frac {h}{e}},\

{\ displaystyle g_ {D} = {\ frac {h} {e}}, \}

Where $h$ ${\ displaystyle h}$ - Planck's constant .

Ammeter Convention ( SI ):

$g_{D}={\frac {hc^{2}}{\varepsilon _{0}}}.$ ${\ displaystyle g_ {D} = {\ frac {hc ^ {2}} {\ varepsilon _ {0}}}.}$

Monopoly Link Constant

It is known that electric charges have a fairly small coupling constant (the so-called fine structure constant ). In the GHS system, it has the following meaning:

\alpha _{E}={\frac {e^{2}}{c\hbar }}\approx 1/137.\

{\ displaystyle \ alpha _ {E} = {\ frac {e ^ {2}} {c \ hbar}} \ approx 1/137. \}

In SI, we have a more cumbersome expression:

\alpha _{E}={\frac {e^{2}}{2hc\varepsilon _{0}}}\approx 1/137,\

{\ displaystyle \ alpha _ {E} = {\ frac {e ^ {2}} {2hc \ varepsilon _ {0}}} \ approx 1/137, \}

Where $\varepsilon _{0}$ ${\ displaystyle \ varepsilon _ {0}}$ - electric constant .

In a similar way, one can introduce the magnetic coupling constant for the GHS system:

\beta _{E}={\frac {g_{D}^{2}}{c\hbar }}={\frac {1}{4\alpha _{E}}}=34{,}25.\

{\ displaystyle \ beta _ {E} = {\ frac {g_ {D} ^ {2}} {c \ hbar}} = {\ frac {1} {4 \ alpha _ {E}}} = 34 {, } 25. \}

For SI there is an expression:

- Weber Convention:

\beta _{E}={\frac {g_{D}^{2}}{2hc\mu _{0}}}={\frac {1}{4\alpha _{E}}}=34{,}25,\

{\ displaystyle \ beta _ {E} = {\ frac {g_ {D} ^ {2}} {2hc \ mu _ {0}}} = {\ frac {1} {4 \ alpha _ {E}}} = 34 {,} 25, \}

- ampere meter convention:

\beta _{E}={\frac {g_{D}^{2}\mu _{0}}{2hc}}={\frac {1}{4\alpha _{E}}}=34{,}25,\

{\ displaystyle \ beta _ {E} = {\ frac {g_ {D} ^ {2} \ mu _ {0}} {2hc}} = {\ frac {1} {4 \ alpha _ {E}}} = 34 {,} 25, \}

Where $\mu _{0}$ ${\ displaystyle \ mu _ {0}}$ Is the magnetic constant of the vacuum. It should be noted here that the magnetic constant is much larger than unity, and therefore the use of perturbative methods in quantum electrodynamics for magnetic charges is not possible.

Monopole Mass

The Dirac theory does not predict the "mass of a magnetic monopole." Therefore, at present, there is no consensus on the estimation of the monopole mass (the experiment only indicates the lower limit). It can also be noted here that the value of the electron mass is a purely experimental fact and is not predicted by the standard model .

Lower Monopole Mass Estimate

The lower bound for the monopole mass can be estimated based on the classical electron radius (SI system):

r_{0}={\frac {e^{2}}{4\pi \varepsilon _{0}m_{0}c^{2}}}={\frac {\alpha _{E}\lambda _{0}}{2\pi }},\

{\ displaystyle r_ {0} = {\ frac {e ^ {2}} {4 \ pi \ varepsilon _ {0} m_ {0} c ^ {2}}} = {\ frac {\ alpha _ {E} \ lambda _ {0}} {2 \ pi}}, \}

Where $\lambda _{0}$ ${\ displaystyle \ lambda _ {0}}$ Is the Compton wavelength of the electron, $m_{0}$ ${\ displaystyle m_ {0}}$ Is the mass of the electron.

Similarly, you can enter a value for the classical radius of a magnetic monopole (SI system (Weber convention)):

r_{D0}={\frac {g_{D}^{2}}{4\pi \mu _{0}m_{D}c^{2}}},\

{\ displaystyle r_ {D0} = {\ frac {g_ {D} ^ {2}} {4 \ pi \ mu _ {0} m_ {D} c ^ {2}}}, \}

Where $m_{D}$ ${\ displaystyle m_ {D}}$ - the mass of the monopole. Thus, by equating the classical radii, we can obtain a lower bound for the monopole mass:

m_{D}=\left({\frac {g_{D}}{e}}\right)^{2}{\frac {\varepsilon _{0}}{\mu _{0}}}m_{0}={\frac {1}{4\alpha _{E}}}m_{0}\approx 4692m_{0}.\

{\ displaystyle m_ {D} = \ left ({\ frac {g_ {D}} {e}} \ right) ^ {2} {\ frac {\ varepsilon _ {0}} {\ mu _ {0}} } m_ {0} = {\ frac {1} {4 \ alpha _ {E}}} m_ {0} \ approx 4692m_ {0}. \}

Attempts to find a monopoly

Repeated attempts to experimentally detect the magnetic monopole were unsuccessful. Particularly intensive searches for a magnetic monopole of cosmic origin have been carried out since the beginning of the 80s of the XX century . Experiments can be divided into several groups.

A magnetic monopole can be detected directly by the magnetic flux associated with it. Passage of magnetic charge $ng_{0}$ ${\ displaystyle ng_ {0}}$ through the superconducting circuit will change the flow to $2\pi \Phi _{0}$ ${\ displaystyle 2 \ pi \ Phi _ {0}}$ where $\Phi _{0}\sim 2\cdot 10^{-3}Gm^{2}$ ${\ displaystyle \ Phi _ {0} \ sim 2 \ cdot 10 ^ {- 3} Gm ^ {2}}$ - a magnetic flux quantum , and the phenomenon of electromagnetic induction will lead to a jump in the current in the circuit, which can be measured using a superconducting quantum interferometer (the so-called " SQUID " - SQUID , Eng. Superconducting Quantum Interference Detector ). According to theoretical estimates, the density of monopoles is so low that one monopole flies through one device per year: on average, one monopole per 10 ²⁹ nucleons . Despite the fact that encouraging events were recorded, in particular the Blas Cabrera event on the night of February 14, 1982 ^[7] (sometimes jokingly called the " Valentine's Day monopole"), these experiments could not be reproduced, and the existence of no monopoles have been established.
A heavy magnetic monopole must have high penetrating power and create strong ionization in its path. Therefore, underground magnetic detectors constructed to study cosmic neutrino fluxes and to search for proton decay were used to search for the magnetic monopole. The probability that a passing monopole will give birth to a photon in the detector is a decreasing function of its mass. Recent experiments at Tevatron ^[8] showed that monopoles with masses less than 600 and 900 GeV , depending on the spin, do not exist, while the upper limit of their mass is 10 ¹⁷ GeV.
They also searched for magnetic monopoles captured in magnetic ores of terrestrial and extraterrestrial origin ( meteorites , the Moon ) of origin ^[9] , as well as tracks left by them in a mica enclosed in ancient terrestrial rocks. Experiments were also aimed at detecting the processes of birth of magnetic monopoles in collisions of high-energy particles at accelerators, however, the masses of such magnetic monopoles are naturally limited by the energy available at modern accelerators. The most severe limitation on the possible number of magnetic monopoles in outer space is given by considerations related to the presence of galactic magnetic fields, since monopoles would be accelerated in these fields, thereby taking away energy from their sources, which would lead to a weakening of the fields with time. A numerical estimate of this limitation depends on a number of assumptions, but it is unlikely that the flux of cosmic magnetic monopoles in a single solid angle can exceed 10 ⁻¹² m ⁻² sr ⁻¹ .

From September to December 2012, the first full-fledged work session of the MoEDAL Large Hadron Collider detector at a collision energy of 8 TeV and a luminosity of 0.75 bn ^{−1 took place} . The search result for magnetic monopoles is negative, but depending on the magnitude of the (magnetic) charge and mass (and it was scanned in the region from 100 GeV to 3.5 TeV), the cross section limit ranged from tens of femtobarns to tens of picobarn ^[10] .

In 2015, the MoEDAL Large Hadron Collider detector searched for magnetic monopoles at a collision energy of 13 TeV. No traces of magnetic monopoles with a mass of up to 6 TeV and a magnetic charge of up to 5 Dirac units were found, the question of their existence remained open ^[11] .

Magnetic Quasi-Monopoles

In some systems, in condensed matter physics, structures may resemble a magnetic monopole — flux tubes. The ends of the magnetic tube form a magnetic dipole, however, since their motion is independent, in many cases they can be approximately considered as independent monopole quasiparticles.

In September 2009, several independent research groups announced the discovery in the solid body ( spin ice from dysprosium titanate Dy ₂ Ti ₂ O ₇ ) of quasiparticles that simulate magnetic monopoles (that is, they look like monopoles at distances significantly exceeding the crystal lattice constant) ^{[12 ]} . In some media and popular science publications, this observation was presented as the detection of magnetic monopoles ^[13] ^[14] .

However, these phenomena are not related ^[15] and, according to a report in Physics World ^[16] , magnetic monopoles found in “spin ice” differ in their origin from the fundamental monopoles predicted by the Dirac theory.

The detected “monopoles” are quasiparticles (magnetic lines of force included in one of these quasiparticles remain closed, passing through a thin “cord” connecting two such quasiparticles, each of which in this sense is not an isolated magnetic charge), and not elementary particles , therefore, this discovery did not revolutionize elementary particle physics . Nevertheless, “quasi-monopoles” are interesting in themselves and are the subject of intensive research. Theoretically, such formations can exist not only in spin ice, but also in the Bose - Einstein condensate . They were discovered by a group of scientists from Boston. They simulated a very cold cloud of Bose gas atoms on a computer. They created a whirlwind from it and got what is very similar to Dirac's monopoly, but not one. Then they were able to create such a vortex in an experiment ^[17] . In January 2014, scientists from the United States and Finland managed to create and photograph a “magnetic monopole” of the same type ^[18] .

Notes

↑ The amazing world inside the atomic nucleus. Questions after the lecture , LPI, September 11, 2007
↑ Fermi, 1952 , p. 115.
↑ Fermi, 1952 , p. 117.
↑ Fermi, 1952 , p. 118.
↑ Polyakov A.M. Particle spectrum in quantum field theory . - M., Letters in JETP, 1974, v. 20, v. 6, pp. 430-433
↑ Curtis G. Callan, Jr. Dyon-fermion dynamics (Eng.) // Phys. Rev. D : journal. - 1982. - Vol. 26 , no. 8 . - P. 2058-2068 . - DOI : 10.1103 / PhysRevD.26.2058 .
↑ Blas Cabrera. First Results from a Superconductive Detector for Moving Magnetic Monopoles (Eng.) // Phys. Rev. Lett. : journal. - 1982. - Vol. 48 , no. 20 . - P. 1378-1381 . - DOI : 10.1103 / PhysRevLett . 48.1378 .
↑ XVI Conference on Charged Particle Accelerators Institute for High Energy Physics.
↑ Strazhev, Tomilchik.
↑ First MoEDAL Experiment Results Published
↑ Magnetic monopoles are not visible even at an energy of 13 TeV
↑ Magnetic monopole takes its first steps (Russian)
↑ Compulence. The existence of magnetic monopoles is confirmed experimentally Archival copy of February 19, 2011 on the Wayback Machine (Russian)
↑ Membrane.ru Magnetic monopole seemed to scientists in spin ice (Russian)
↑ Magnetic monopoles spotted in spin ices, September 3, 2009. "Oleg Chernyshev, a researcher at Johns Hopkins University, emphasizes that this theory and experiments are specific to spin ice and are unlikely to shed light on the magnetic monopoles predicted by Dirac."
↑ physicsworld.com Magnetic monopoles spotted in spin ices
↑ Quantum cloud simulates magnetic monopole: Nature News & Comment
↑ Scientists have created a single pole magnet

Literature

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Strazhev V.I., Tomilchik L.M. Electrodynamics with magnetic charge. - Minsk, 1975.
Coleman S. The Magnetic Monopole Fifty Years Later . - Per. from English - Advances in Physical Sciences , 1984, v. 144 , p. 277.
Devons S. Searches for the magnetic monopole . - Advances in Physical Sciences , 1965, v. 85 , c. 4, p. 755-760 (Addition of B. M. Bolotovsky, ibid., Pp. 761-762)
Schwinger Yu. Magnetic model of matter . - Advances in Physical Sciences , 1971, v. 103 , c. 2, p. 355-365.
Shnir, Yakov M. Magnetic Monopoles. - Springer-Verlag, Berlin, 2005, ISBN 3-540-25277-0
Adventures of the great equations of the MOO "Science and Technology"
Yakymakha OL (1989). High Temperature Quantum Galvanomagnetic Effects in the Two-Dimensional Inversion Layers of MOSFET's (In Russian). Kyiv: Vyscha Shkola. p. 91. ISBN 5-11-002309-3 .
DJP Morris, et all. Dirac Strings and Magnetic Monopoles in the Spin Ice Dy2Ti2O7. Science October 16, 2009.
LDC Jaubert, PCW Holdsworth. Signature of magnetic monopole and Dirac string dynamics in spin ice. Nature Physics 5, 258-261 (2009).
G. Giacomelli and L. Patrizii. Magnetic Monopole Searches. arXiv: hep-ex / 0302011v2.
Zhong, Fang; Naoto Nagosa, Mei S. Takahashi, Atsushi Asamitsu, Roland Mathieu, Takeshi Ogasawara, Hiroyuki Yamada, Masashi Kawasaki, Yoshinori Tokura, Kiyoyuki Terakura (October 3, 2003). "The Anomalous Hall Effect and Magnetic Monopoles in Momentum Space." Science 302 (5642): 92-95. doi: 10.1126 / science.1089408. ISSN 1095-9203. Retrieved on 2 August 2007
Making magnetic monopoles, and other exotica, in the lab
Xiao-Liang Qi, Rundong Li, Jiadong Zang, Shou-Cheng Zhang. Science Express magazine, 29 January 2009 Inducing a Magnetic Monopole with Topological Surface States
C. Castelnovo, R. Moessner and SL Sondhi, Nature 451, 42-45 (3 January 2008) Magnetic monopoles in spin ice
Steven Bramwell et al. Nature 461, 956-959 (October 15, 2009); doi: 10.1038 / nature08500
Science Daily , September 4, 2009 Magnetic Monopoles Detected In A Real Magnet For The First Time
DJP Morris, DA Tennant, SA Grigera, B. Klemke, C. Castelnovo, R. Moessner, C. Czternasty, M. Meissner, KC Rule, J.-U. Hoffmann, K. Kiefer, S. Gerischer, D. Slobinsky, and RS Perry. Dirac Strings and Magnetic Monopoles in Spin Ice Dy ₂ Ti ₂ O ₇ . Science , 4 September 2009 [1]
Fermi E. Lectures in atomic physics. - M .: IL, 1952. - 123 p.

Links

Half of the magnet Vladislav Kobychev, Sergey Popov “Popular Mechanics” No. 2, 2015 Archive

[elementyGrav-1] The amazing world inside the atomic nucleus. Questions after the lecture , LPI, September 11, 2007

[_5de1db0bade00a33-2] Fermi, 1952 , p. 115.

[_5de1db0bade00a31-3] Fermi, 1952 , p. 117.

[_5de1db0bade00a3e-4] Fermi, 1952 , p. 118.

[5] Polyakov A.M. Particle spectrum in quantum field theory . - M., Letters in JETP, 1974, v. 20, v. 6, pp. 430-433

[6] Curtis G. Callan, Jr. Dyon-fermion dynamics (Eng.) // Phys. Rev. D : journal. - 1982. - Vol. 26 , no. 8 . - P. 2058-2068 . - DOI : 10.1103 / PhysRevD.26.2058 .

[7] Blas Cabrera. First Results from a Superconductive Detector for Moving Magnetic Monopoles (Eng.) // Phys. Rev. Lett. : journal. - 1982. - Vol. 48 , no. 20 . - P. 1378-1381 . - DOI : 10.1103 / PhysRevLett . 48.1378 .

[web.ihep.su-8] XVI Conference on Charged Particle Accelerators Institute for High Energy Physics.

[9] Strazhev, Tomilchik.

[10] First MoEDAL Experiment Results Published

[11] Magnetic monopoles are not visible even at an energy of 13 TeV

[12] Magnetic monopole takes its first steps (Russian)

[13] Compulence. The existence of magnetic monopoles is confirmed experimentally Archival copy of February 19, 2011 on the Wayback Machine (Russian)

[14] Membrane.ru Magnetic monopole seemed to scientists in spin ice (Russian)

[15] Magnetic monopoles spotted in spin ices, September 3, 2009. "Oleg Chernyshev, a researcher at Johns Hopkins University, emphasizes that this theory and experiments are specific to spin ice and are unlikely to shed light on the magnetic monopoles predicted by Dirac."

[16] ysicsworld.com Magnetic monopoles spotted in spin ices

[17] Quantum cloud simulates magnetic monopole: Nature News & Comment

[18] Scientists have created a single pole magnet