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Пишет друг друга пердуна ([info]oort)
@ 2018-11-22 13:05:00


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Кстати а кто-нибудь знает,
в природе (настоящей природе) встречаются электромагнитные инстантоны?
то есть поля замкнутых автодуальных 2-форм F

F=*F
dF=0

где F это тензор электромагнитного поля
также известный как кривизна связности, известной под именем электромагнитного потенциала
типа F=E_xdxdt+E_ydydt+E_zdzdt+B_xdydz+B_ydzdx+B_zdxdy

и если просто взять звездочку Ходжа и прировнять то получится странная штука что он меняет местами электрические и магнитные поля

B_i -> E_i
E_i -> -B_i

то есть они получается должны нулевые быть?


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[info]tiphareth
2018-11-23 20:29 (ссылка)
https://www.nature.com/articles/nature12954
Observation of Dirac monopoles in a synthetic magnetic field

Magnetic monopoles—particles that behave as isolated north or south magnetic poles—have been the subject of speculation since the first detailed observations of magnetism several hundred years ago1. Numerous theoretical investigations and hitherto unsuccessful experimental searches2 have followed Dirac’s 1931 development of a theory of monopoles consistent with both quantum mechanics and the gauge invariance of the electromagnetic field3. The existence of even a single Dirac magnetic monopole would have far-reaching physical consequences, most famously explaining the quantization of electric charge3,4. Although analogues of magnetic monopoles have been found in exotic spin ices5,6 and other systems7,8,9, there has been no direct experimental observation of Dirac monopoles within a medium described by a quantum field, such as superfluid helium-3 (refs 10, 11, 12, 13). Here we demonstrate the controlled creation14 of Dirac monopoles in the synthetic magnetic field produced by a spinor Bose–Einstein condensate. Monopoles are identified, in both experiments and matching numerical simulations, at the termini of vortex lines within the condensate. By directly imaging such a vortex line, the presence of a monopole may be discerned from the experimental data alone. These real-space images provide conclusive and long-awaited experimental evidence of the existence of Dirac monopoles. Our result provides an unprecedented opportunity to observe and manipulate these quantum mechanical entities in a controlled environment.

https://en.wikipedia.org/wiki/Magnetic_monopole#Searches_for_magnetic_monopoles

Searches for magnetic monopoles

Experimental searches for magnetic monopoles can be placed in one of two categories: those that try to detect preexisting magnetic monopoles and those that try to create and detect new magnetic monopoles.

Passing a magnetic monopole through a coil of wire induces a net current in the coil. This is not the case for a magnetic dipole or higher order magnetic pole, for which the net induced current is zero, and hence the effect can be used as an unambiguous test for the presence of magnetic monopoles. In a wire with finite resistance, the induced current quickly dissipates its energy as heat, but in a superconducting loop the induced current is long-lived. By using a highly sensitive "superconducting quantum interference device" (SQUID) one can, in principle, detect even a single magnetic monopole.

According to standard inflationary cosmology, magnetic monopoles produced before inflation would have been diluted to an extremely low density today. Magnetic monopoles may also have been produced thermally after inflation, during the period of reheating. However, the current bounds on the reheating temperature span 18 orders of magnitude and as a consequence the density of magnetic monopoles today is not well constrained by theory.

There have been many searches for preexisting magnetic monopoles. Although there have been tantalizing events recorded, in particular the event recorded by Blas Cabrera on the night of February 14, 1982 (thus, sometimes referred to as the "Valentine's Day Monopole"[36]), there has never been reproducible evidence for the existence of magnetic monopoles.[13] The lack of such events places an upper limit on the number of monopoles of about one monopole per 1029 nucleons.

Another experiment in 1975 resulted in the announcement of the detection of a moving magnetic monopole in cosmic rays by the team led by P. Buford Price.[12] Price later retracted his claim, and a possible alternative explanation was offered by Alvarez.[37] In his paper it was demonstrated that the path of the cosmic ray event that was claimed due to a magnetic monopole could be reproduced by the path followed by a platinum nucleus decaying first to osmium, and then to tantalum.

High energy particle colliders have been used to try to create magnetic monopoles. Due to the conservation of magnetic charge, magnetic monopoles must be created in pairs, one north and one south. Due to conservation of energy, only magnetic monopoles with masses less than the center of mass energy of the colliding particles can be produced. Beyond this, very little is known theoretically about the creation of magnetic monopoles in high energy particle collisions. This is due to their large magnetic charge, which invalidates all the usual calculational techniques. As a consequence, collider based searches for magnetic monopoles cannot, as yet, provide lower bounds on the mass of magnetic monopoles. They can however provide upper bounds on the probability (or cross section) of pair production, as a function of energy.

The MoEDAL experiment, installed at the Large Hadron Collider, is currently searching for magnetic monopoles and large supersymmetric particles using nuclear track detectors and aluminum bars around LHCb's VELO detector. The particles it is looking for damage the plastic sheets that comprise the nuclear track detectors along their path, with various identifying features. Further, the aluminum bars can trap sufficiently slowly moving magnetic monopoles. The bars can then be analyzed by passing them through a SQUID.

The Russian astrophysicist Igor Novikov claims the fields of macroscopic black holes are potential magnetic monopoles, representing the entrance to an Einstein–Rosen bridge.[38]

"Monopoles" in condensed-matter systems

Since around 2003, various condensed-matter physics groups have used the term "magnetic monopole" to describe a different and largely unrelated phenomenon.[18][19]

A true magnetic monopole would be a new elementary particle, and would violate Gauss's law for magnetism ∇⋅B = 0. A monopole of this kind, which would help to explain the law of charge quantization as formulated by Paul Dirac in 1931,[39] has never been observed in experiments.[40][41]

The monopoles studied by condensed-matter groups have none of these properties. They are not a new elementary particle, but rather are an emergent phenomenon in systems of everyday particles (protons, neutrons, electrons, photons); in other words, they are quasi-particles. They are not sources for the B-field (i.e., they do not violate ∇⋅B = 0); instead, they are sources for other fields, for example the H-field,[5] the "B*-field" (related to superfluid vorticity),[6][42] or various other quantum fields.[43] They are not directly relevant to grand unified theories or other aspects of particle physics, and do not help explain charge quantization—except insofar as studies of analogous situations can help confirm that the mathematical analyses involved are sound.[44]

There are a number of examples in condensed-matter physics where collective behavior leads to emergent phenomena that resemble magnetic monopoles in certain respects,[17][45][46][47] including most prominently the spin ice materials.[5][48] While these should not be confused with hypothetical elementary monopoles existing in the vacuum, they nonetheless have similar properties and can be probed using similar techniques.

Some researchers use the term magnetricity to describe the manipulation of magnetic monopole quasiparticles in spin ice,[48][49] in analogy to the word "electricity".

One example of the work on magnetic monopole quasiparticles is a paper published in the journal Science in September 2009, in which researchers described the observation of quasiparticles resembling magnetic monopoles. A single crystal of the spin ice material dysprosium titanate was cooled to a temperature between 0.6 kelvin and 2.0 kelvin. Using observations of neutron scattering, the magnetic moments were shown to align into interwoven tubelike bundles resembling Dirac strings. At the defect formed by the end of each tube, the magnetic field looks like that of a monopole. Using an applied magnetic field to break the symmetry of the system, the researchers were able to control the density and orientation of these strings. A contribution to the heat capacity of the system from an effective gas of these quasiparticles was also described.[16][50] This research went on to win the 2012 Europhysics Prize for condensed matter physics.

In another example, a paper in the February 11, 2011 issue of Nature Physics describes creation and measurement of long-lived magnetic monopole quasiparticle currents in spin ice. By applying a magnetic-field pulse to crystal of dysprosium titanate at 0.36 K, the authors created a relaxing magnetic current that lasted for several minutes. They measured the current by means of the electromotive force it induced in a solenoid coupled to a sensitive amplifier, and quantitatively described it using a chemical kinetic model of point-like charges obeying the Onsager–Wien mechanism of carrier dissociation and recombination. They thus derived the microscopic parameters of monopole motion in spin ice and identified the distinct roles of free and bound magnetic charges.[49]

In superfluids, there is a field B*, related to superfluid vorticity, which is mathematically analogous to the magnetic B-field. Because of the similarity, the field B* is called a "synthetic magnetic field". In January 2014, it was reported that monopole quasiparticles[51] for the B* field were created and studied in a spinor Bose–Einstein condensate.[6] This constitutes the first example of a quasi-magnetic monopole observed within a system governed by quantum field theory.[44]

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[info]oort
2018-11-26 14:19 (ссылка)
ochen interesno!

no moy vopros byl bolee down to earth -- na samom dele na R^4 deystvitel'no ne byvaet instantonov s abelevoy kalibrovochnoy gruppoy

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