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Magnetic Monopoles in Field Theory and cosmology

Many theories of particle physics beyond the standard model predict the existence of magnetic monopoles. There has been no experimental or observational sign of them in spite of extensive searches. In this paper Rajantie reviewed the role of magnetic monopoles in quantum field theory and discusses their implications for particle physics and cosmology. Rajantie also highlights their differences and similarities with magnetic monopoles found in frustrated magnetic systems.

It is expected, based on experience, that it is not possible to separate magnetic north from magnetic south into separate magnetic monopoles, i.e. isolated magnetic charges. Peregrinus discussed this in the 13^th century (Peregrinus, 1904, translated). Nevertheless, there are strong theoretical reasons to believe that they should exist.

The possibility of free magnetic charges was speculated about in 1894 (Curie, 1894), and magnetic monopoles were used occasionally in mathematical examples in electrodynamics, though they were only considered seriously by physicists after it had been shown in 1931 that if they existed it would explain the quantisation of electric charge (Dirac, 1931). Magnetic monopoles were shown to exist as nonlinear objects in many particle physics theories (‘t Hooft, 1974; Polyakov, 1974). They are, in fact, an inevitable prediction of grand unification of elementary particle interactions (Preskill, 1979) and the same also applies generally to ‘theories of everything’ that are more modern, such as superstring theory (Duff, Khuri & Lu, 1995).

According to Rajantie it would be an incredible breakthrough in high-energy physics to find a magnetic monopole. The properties of magnetic monopoles are derived from processes taking place at very high energies, though as they are stable particles and they interact through the electromagnetic field, they would be relatively easy to study experimentally. They could, therefore, open up a new window to particle physics at energies that are out of reach of any foreseeable accelerator experiments. There have been many unsuccessful attempts to detect them in different ways (Nakamura et al., 2010; Giacomelli, Patrizii & Sahnoun, 2011).

Magnetic monopoles have played an important role in theoretical high energy physics, though they have not been found. Magnetic monopoles have provided powerful theoretical tools to investigate properties of strongly coupled non-Abelian gauge field theories, e.g. quantum chromodynamics (QCD) and especially the supersymmetric variants of it (Shifman & Yung, 2007). There was an attempt to explain why magnetic monopoles are apparently absent which led to the formulation of the theory of cosmological inflation (Guth, 1981), which was confirmed later by astronomical observations (Komatsu et al., 2011).

It has recently been discovered that spin ices, frustrated magnetic systems, have effective quasi-particle excitations that have magnetic charges (Castelnovo, Moessner & Sondhi, 2008). It appears these effective monopoles have very similar properties to actual fundamental magnetic monopoles (Jaubert & Holdsworth, 2009; Bramwell et al., 2000), which may also provide a way of learning more about their physics.

This paper was aimed at giving a brief overview of magnetic monopoles in particle physics. See (Rajantie, 2012) for a more pedagogical introduction, and for a more detailed review, see (Milton, 2006). There is also a comprehensive and up-to-date magnetic monopole bibliography available (Balestra et al., 2011).

Conclusions

Rajantie says the study of magnetic monopoles has been a great success as well as a disappointment. Theoretical monopole solutions and the use of electric-magnetic duality have provided theorists with new ways to understand the physics of gauge field theories. The theory of inflation, the cornerstone of modern cosmology, was also led to by the absence of magnetic monopoles in the Universe.

The discovery recently of effective magnetic monopole quasi-particles in spin-ices raises the question of whether it could be possible to make use of them to take these theoretical advances further. Though there are important difference between fundamental magnetic monopole particles and the quasi-particles, the quasi-particles behave in many ways as do the fundamental magnetic monopole particles. Possibly most importantly, the Dirac strings that connect the monopoles are not completely unphysical.

This does not mean that spin ice experiments cannot be used to draw conclusions for fundamental monopoles, though the physicist needs to be aware of the differences between the systems and the limitations they impose. Rajantie suggests situations in which random thermal fluctuations play an important role would therefore appear to be most promising, e.g. studying the formation of monopoles in phase transitions.  

Sources & Further reading

Rajantie, A. (2012). "Magnetic monopoles in field theory and cosmology." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370(1981): 5705-5717.