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{{Short description|Equations describing magnetic monopoles}} ...ge theory (mathematics)|gauge theory]], the '''Bogomolny equation''' for [[magnetic monopole]]s is the equation ...

{{Short description|Flow of magnetic monopole charge}} ...out|a current of magnetic monopoles|current as an analog for magnetic flux|Magnetic circuit}} ...

...1=C. |last2=Moessner |first2=R. |last3=Sondhi |first3=S.L. |title=Magnetic Monopoles in Spin Ice |journal=Nature |date=3 January 2008 |volume=451 |issue=7174 |p ...Alan Tennant, for the prediction and experimental observation of magnetic monopoles in spin ice.<ref>{{cite news |title=2012 EPS CMD Europhysics Prize |url=htt ...

...] that is a dual of the [[photon]] under [[Montonen–Olive duality|electric–magnetic duality]] which is predicted by some theoretical models,<ref name="bliokh"> ...is not dual symmetric (i.e. symmetric under rotation between electric and magnetic charges) which causes problems for the [[energy–momentum tensor|energy–mome ...

...hesized as dual of [[graviton]] under [[electric-magnetic duality|electric–magnetic duality]] in [[supergravity]]. | Dual of the [[photon]] under [[Montonen–Olive duality|electric–magnetic duality]] ...

Disordered magnetic materials were later shown to form interesting spin phases. Spin fractiona ...ub>7</sub> has fractionalized spin freedom, leading to deconfined magnetic monopoles.<ref>{{cite journal ...

...magnetic field]]s are constrained to move together in the limit of large [[magnetic Reynolds number]]s. It is named after [[Hannes Alfvén]], who put the idea f ...nnot change. This approximation breaks down in [[current sheet]]s, where [[magnetic reconnection]] can occur. ...

...of the success of the dictionary is that it allowed the understanding of [[Magnetic monopole#Dirac's quantization|monopole quantization]] in terms of [[Hopf fi ...ivalence between a quantization condition for [[Magnetic monopole|magnetic monopoles]] used by [[Paul Dirac]] back in 1931 and [[Hopf fibration]], a fibration o ...

...mer is much longer than the latter. [[Albert Einstein]] showed that the [[magnetic field]] arises through the [[Classical electromagnetism and special relativ ...ns. [[Electrostatics]] deals only with stationary [[electric charge]]s so magnetic fields do not arise and are not considered. [[Permanent magnet]]s can be d ...

...ath>\mathbf B</math> there are no sources or sinks because there are no [[magnetic monopole]]s as described by [[Gauss's law for magnetism]] which states that ...ooks.google.com/books?id=ecKdEAAAQBAJ&dq=there+are+no+sources+and+sinks+of+magnetic+field&pg=PA516 |title=Further Mathematics for the Physical Sciences |last2= ...

...'''), used as the definition of the [[electric field|'''E''' field]] and [[magnetic field|'''B''' field]].]] ...rength, Wb (Weber) and A m (Ampere metre). Dimensional analysis shows that magnetic charges relate by ''q_m''(Wb) = ''μ''₀ ''q_m ...

.../s002200050490| s2cid=14125789 }}</ref> noncommutative [[Magnetic monopole|monopoles]] and monopole strings with [[David Gross]] in 2000 and for his work with [ ...

...</math>, one obtains the [[Bogomolny equations]] which describe [[magnetic monopoles]] on <math>\mathbb{R}^3</math>. ...f><ref>Donaldson, S. K. (1984). Nahm's equations and the classification of monopoles. Communications in Mathematical Physics, 96(3), 387–408.</ref> ...

...in the same manner as for [[Electric field|electric]] and [[Magnetic field|magnetic]] fields where the monopole is essentially the first non-trivial (e.g. cons Dual to the case above of line sources, vortex lines play the role of monopoles for [[irrotational flow]]s. ...

...les, vortices or textures can arise. It was debated for quite a while if [[magnetic monopole]]s might be residuals of defects in the symmetry-broken Higgs fiel ...d [[disclination]]s in two dimensions. The latter are nothing else but the monopoles of the high-symmetry phase within the six-fold director field of crystal ax ...

...g |first1=David |title=Final Steps to the Field Theory: Faraday's Study of Magnetic Phenomena, 1845-1850 |journal=Historical Studies in the Physical Sciences | ...etism]]. He realized that [[Electric field|electric]] and [[magnetic field|magnetic]] fields are not only fields of force which dictate the motion of particles ...

...interact with normal matter through either the [[nuclear force]] or their magnetic moments, with the charged proton also interacting by the [[Coulomb force]]. ...ents of molecules by [[proton nuclear magnetic resonance]]. The neutron's magnetic moment is exploited to probe the atomic structure of materials using scatte ...

...ory with structure group the [[circle group]]. Work of [[Paul Dirac]] on [[magnetic monopole]]s and relativistic [[quantum mechanics]] encouraged the idea that ...[[Vafa–Witten invariants]].<ref name=seibergwitten>Witten, Edward (1994), "Monopoles and four-manifolds.", Mathematical Research Letters, 1 (6): 769–796, arXiv: ...

...ing the Topological Low-Energy Physics of the F Model in a Two-Dimensional Magnetic Lattice |url=https://link.aps.org/doi/10.1103/PhysRevLett.129.027202 |journ ...

..., [[gauge theory]], [[mathematical physics]], [[Magnetic monopole|magnetic monopoles]] ...K. |date=September 1984 |title=Nahm's equations and the classification of monopoles |url=http://link.springer.com/10.1007/BF01214583 |journal=Communications in ...