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rpp2010-rev-mag-monopole-searches - 1 MAGNETIC MONOPOLES...

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–1– MAGNETIC MONOPOLES Written in September 2009 by D. Milstead (Stockholm Univ.) and E.J. Weinberg (Columbia Univ.). The symmetry between electric and magnetic felds in the sourceFree Maxwell’s equations naturally suggests that electric charges might have magnetic counterparts, known as magnetic monopoles. Although the greatest interest has been in the supermassive monopoles that are a frm prediction oF all grand unifed theories, one cannot exclude the possibility oF lighter monopoles, even though there is at present no strong theoretical motivation For these. In either case, the magnetic charge is constrained by a quantization condition frst Found by Dirac [1]. Consider a monopole with magnetic charge Q M and a Coulomb magnetic feld B = Q M 4 π ˆ r r 2 . (1) Any vector potential A whose curl is equal to B must be singular along some line running From the origin to spatial infnity. This Dirac string singularity could potentially be detected through the extra phase that the waveFunction oF a particle with electric charge Q E would acquire iF it moved along a loop encircling the string. ±or the string to be unobservable, this phase must be a multiple oF 2 π . Requiring that this be the case For any pair oF electric and magnetic charges gives the condition that all charges be integer multiples oF minimum charges Q min E and Q min M obeying Q min E Q min M =2 π. (2) (±or monopoles which also carry an electric charge, called dyons, the quantization conditions on their electric charges can be modifed. However, the constraints on magnetic charges, as well as those on all purely electric particles, will be unchanged.) Another way to understand this result is to note that the conserved orbital angular momentum oF a point electric charge moving in the feld oF a magnetic monopole has an additional component, with L = m r × v 4 πQ E Q M ˆ r (3) CITATION: K. Nakamura et al. (Particle Data Group), JPG 37 , 075021 (2010) (URL: http://pdg.lbl.gov) July 30, 2010 14:34
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–2– Requiring the radial component of L to be quantized in half- integer units yields Eq. (2). If there are unbroken gauge symmetries in addition to the U(1) of electromagnetism, the above analysis must be modiFed [2,3]. ±or example, a monopole could have both a U(1) magnetic charge and a color magnetic charge. The latter could combine with the color charge of a quark to give an additional contribution to the phase factor associated with a loop around the Dirac string, so that the U(1) charge could be the Dirac charge Q D M 2 π/e , the result that would be obtained by substituting the electron charge into Eq. (2). On the other hand, for monopoles without color-magnetic charge, one would simply insert the quark electric charges into Eq. (2) and conclude that Q M must be a multiple of 6 .
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