Magnetic monopoles and grand unified theories springerlink. Magnetic monopoles have since been studied in more general, socalled unified field theories, in which they could exist in the absence of a terminating vortex. Pdf magneticmonopole excitations in the georgiglashow model. Symmetries, symmetry breaking, gauge theory and the boson. The energye of the static system is calculable and it is either zero or infinite. It is suggested that the magnetic monopoles predicted by grand unified theories would not be produced in significant numbers if electromagnetic gauge invariance is spontaneously broken when the temperature t is greater than tc. The magnetic photon couples via vector coupling with monopoles. Abelian gauge theory qed electrodynamics is example of most simple u1. The discovery by a candidate event in a single superconducting loop in 1982 6 stimulated an enormous experimental e ort to search for supermassive magnetic monopoles 3,4,5. This elusive particle was predicted to exist long ago and helped explain why the universe works the way it does, but it took decades for us to detect.
Oct 25, 2010 magnetic monopoles outed, powerless to help grand unified theory magnetic monopoles are cropping up in a material called spin ice, but their casey johnston oct 25, 2010 7. Pdf monopole operators and hilbert series of coulomb. Recently monopoles have become indispensable in many gauge theories, which endow them with a variety of extraordinarily large masses. According to his model the photon couples via vector coupling with leptons and hadrons, but not with monopoles.
We have thus calculated the mass of a magnetic monopole, by both analytical and numerical means. A hypothetical particle which would be the magnetic analog of charged particles carrying magnetic charge. The exact static, spherically symmetric solutions of the magnetic monopoles in both yangmills and unified gauge theories are obtained. The stability of the classical monopole solution is ensured by a topological principle to. Magnetic monopoles outed, powerless to help grand unified. A magnetic monopole would have a net magnetic charge. Gauge theories in 4d adding extra dimension kaluzaklein theory 5d scalar theory and boundary conditions future plans references. In this second lecture we describe the physics of t hooftpolyakov magnetic monopoles when embedded in supersymmetric sun gauge theories. Magnetic monopole solutions seem to fit into grand unified theories like a piece of a jigsaw. Mathematically this means that we are studying a principal u1bundle with connection aover spacetime in general, a riemannian manifold. Physicists create synthetic magnetic monopoles in the lab. Magnetic monopoles in su3 gauge theories sciencedirect. Magnetic monopoles gauge theories physics stack exchange. Calculating the mass of magnetic monopoles in nonabelian.
The quantization condition magnetic charge must come in quanta of a given size, just as electric charge does. Nuyts department of physics, university of mons received 19 december 1975 t hooft constructed a finite mass unit. It is shown that in all those gauge theories in which the electromagnetic group ui is taken to be a subgroup of a larger group with a compact covering group, like su2 or su3, genuine magnetic monopoles can be created as. The general answer to the question is that it is known how to construct a quantum mechanical theory of magnetic monopoles acting as individual particles among themselves and also perturbatively in the background of the standard model fields.
Then the degrees of freedom are abelian gauge fields, gluons, quarks, and magnetic monopoles. It is shown that in all those gauge theories in which the electromagnetic group u 1 is taken to be a subgroup of a larger group with a compact. An account is given of the new insight into the theory of magnetic monopoles originating from the work of t hooft 1976 and polyakov 1974. The easiest way to visualize a magnetic monopole is by considering a pole of a long, thin magnet or an end point of a long, thin solenoid. The first part of my talk is devoted to explaining why magnetic monopoles, for so long a theoretical curiosity, arise naturally in the grand unified gauge theories, currently thought to be a step on the way to ultimate synthesis of physics. The simplest of these is electromagnetism, which has gauge group u1. The gauge noninvariance of classical electromagnetism. Theoretical studies of magnetic monopole from maxwell to nonperturbative lattice formulation summer, 20 written by yun shi supervised by dr arttu rajentie imperial college london submitted in the partial ful llment of the requirements for the degree of master of science in theoretical physics of imperial college london. The best experimental upper limit, obtained by searching for induced currents in superconducting wires, is 1 monopole per 10 29 nucleons jeon and longo 1995. It is shown that in all those gauge theories in which the electromagnetic group u 1 is taken to be a subgroup of a larger group with a compact covering group, like su2 or su3, genuine magnetic monopoles can be created as regular solutions of the field equations.
Although, in the absence of any observation ofa monopole, they might seem to be an inconvenience, they are intimately related to one of the frequently cited motivations for unification, namely to provide an explanation for electric charge quantization. Introduction two reasons can be given for the recent upsurge of interest in the theory of magnetic monopoles. Now, however, we take as a gauge condition that the higgs field is 20, 0 times this vector. When blacketts idea was abandoned, attention was confined to. However they are obtained in spontaneously broken gauge theories which in general have elctric charges in their spectrum. However, the key step in the rehabilitation of magnetic monopoles was the. A twophoton model has already been suggested by salam15. The existence of the magnetic monopole solution is a consequence of symmetry rather than dynamics. Olive cern, geneva niels bohr institute, copenhagen d. The geometry and dynamics of magnetic monopoles on jstor. Monopole dynamics and hyperkahler geometry physical background. Mills theory and see how it has played a role in the development of modern gauge theories. Descriptions of magnetic monopoles in the modern physics lead to the strongweak coupling duality that relates a theory that describes a strong force to another theory of magnetic monopoles and electric magnetic duality. Holism and structuralism in u1 gauge theory 4 mations.
Modern interest in the concept stems from particle theories, notably the grand unification theory and superstring theory, which predict their existence. Fairlie department of mathematics, university of durham, uk j. Let us choose our coordinates such that the pole is at the origin and the magnet goes along the negative z semiaxis. In this derivation he uses a vector potential to represent the. In section 7 we briefly comment the unified electroweak gauge model and the the higgs mechanism proposed by weinbergsalam that explains the masses of the vectorial bosons w and zo. The word gauge means a measurement, a thickness, an in between distance as in railroad tracks, or a resulting number of units per certain parameter a number of loops in an inch of fabric or a number of lead balls in a pound of ammunition. Magnetic charge quantization from sym considerations arxiv. One was the possible experimental observation of such an. The only gauge group that satis es these four conditions is the group u1 u01. Modern theories describe physical forces in terms of fields, e. In fact, magnetic monopoles appear in spontaneously broken unified gauge theories even in the classical limit, as stable time independent. The mass of magnetic monopoles is of great importance when conducting experiments designed to.
Elementary particle physics from theory to experiment. Theoretical and experimental status of magnetic monopoles kimball a milton department of physics, washington university, st. The nonphysical view concerning the vector potential a in classical electromagnetic theory is the likely reason for using 3 to represent the magnetic monopole field. Theory of magnetic monopoles and electricmagnetic duality. In this paper we will discuss the uses of gauge theory and the meaning of gauge invariance. Many theories predict existence of magnetic monopoles, but. The gauge field lagrangian gauge invariant lagrangians for spin0 and sping.
The word gauge means a measurement, a thickness, an inbetween distance as in railroad tracks, or a resulting number of units per certain parameter a number of loops in an inch of fabric or a number of lead balls in a pound of ammunition. It is shown that in all those gauge theories in which the electromagnetic group ui. Gauge theories in extra dimensions and deconstruction. Two of the original strings, oriented in the same direction, can now annihilate by formation of a monopole pair 5. Particle physics studies the smallest pieces of matter, 1 110. Their magnetic monopole, associated with the conventional electromagnetic gauge group u1, occurs as a finiteenergy smooth soliton solution to. Magnetic monopoles in unified gauge theories inspire. The magnetic monopole is a hypothetical particle in physics that is a magnet with only one pole.
We know the gauge invariance of maxwells equations of. Aug 09, 2016 youve probably heard of the higgs boson. Descriptions of magnetic monopoles in the modern physics lead to the strongweak coupling duality that relates a theory that describes a strong force to another theory of magnetic monopoles and electricmagnetic duality. Magnetic monopoles with multiple dirac charge are found to be stablein grand unified theories. Symmetries, symmetry breaking, gauge theory and the boson of. The charge on magnetic monopoles predicted by guts is either 1 or jeon and longo 1995. It is shown that in all those gauge theories in which the electromagnetic group ui is taken to be a subgroup of a larger group with a compact covering group, like su2 or su3, genuine magnetic monopoles can be. Finally, on the basis of laboratory experiments, blackett himself abandoned the idea in 1952.
In more technical terms, it would have a net magnetic charge. Magnetic monopoles in unified gauge theories science. Thus gauge theories of the unified interactions demand the existence of mms. Magnetic monopoles and group theory welcome to scipp. First there was the 1998 d0 limit on the virtual production of monopoles. As the mass of the monopole proposed by dirac in 1931 is a free parameter, we have instead studied the monopole put forward by t hooft. Attempts to settle the question by determining the vertical gradient of the field, however, gave contradictory results.
This answer is based on david tongs lectures on solitons chapter 2 monopoles. Hooft showed, where m v is gauge boson mass monopoles arise in guts, with mass of the scale of the symmetry breaking of the theory su5. Their magnetic monopole, associated with the conventional electromagnetic gauge group u1, occurs as a finiteenergy smooth soliton solution to an su2 gauge theory. The purpose of these lectures is to give an introduction to gauge theories and the standard 14. We carry out the abelian projection of sun gauge theories, both in the continuum and on the lattice. The prototype model for su 2 u1 electroweak interactions. In particle physics, a magnetic monopole is a hypothetical elementary particle that is an isolated magnet with only one magnetic pole a north pole without a south pole or vice versa.
The gauge noninvariance of classical electromagnetism 391 theorem to evaluate. However, dirac1 demonstrated that quantum mechanics apparently predicts that a magnetic charge, if it is ever found in nature, must be quantized in units of hc2e where e is the absolute electron charge value. If the unbroken gauge group has a u1 factor one might expect magnetic monopole solutions to exist. In the second part, an ontological underdetermination of gauge theories is carved out. Quantum mechanics does not require magnetic monopoles to exist.
Magnetic monopoles in grand unified theories inspire. Modern interest in the concept stems from particle theories, notably the grand unified and superstring. Stable grandunified monopoles with multiple dirac charge chicago. We study the magnetic monopoles in nonabelian gauge theories. The stability of the classical monopole solution is ensured by a topological principle to be explained in detail below. And because the existence of a magnetic monopole would imply a duality between electricity and magnetism, the theory suggesting magnetic monopoles becomes almost intoxicating. Some grand unified theories guts predict the existence of small numbers of these particles thooft 1974, polyakov 1974.
Theoretical and experimental status of magnetic monopoles. Demanding that the asymptotic form of the u1 gauge. However, the vector potential a1 in 3 does not posses this symmetry. Since diracs day, many theories have made predictions about the properties of magnetic monopoles. Solitons finiteenergy, nondissipative solutions of the classical wave equations cannot arise in linear theories such as electrodynamics, because there is dispersion non linear theories allow cancelation of dispersive effects. Magnetic monopoles outed, powerless to help grand unified theory magnetic monopoles are cropping up in a material called spin ice, but their casey johnston oct 25, 2010 7. Magnetic monopoles in unified gauge theories sciencedirect. In the usual gauge theories one normally chooses the gauge in which the higgs field is a vector in a fixed direction, say, along the positive z axis, in isospin space. Gut monopoles are too massive to be produced in accelerators, but could have been produced in early universe monopole searches focus on accelerators, cosmic. Sep 22, 2016 since diracs day, many theories have made predictions about the properties of magnetic monopoles. It is shown that in all those gauge theories in which the electromagnetic group u1 is taken to be a subgroup of a larger group with a compact. Nuyts department of physics, university of mons received 19 december 1975 t hooft constructed a finite mass unit monopole by a. Grand unified theories predict monopoles that would be over 10 quadrillion times more massive.
An account is given of the new insight into the theory of magnetic monopoles originating from the work of. Magnetic monopoles in gauge field theories iopscience. Exact magnetic monopole solutions in yangmills and unified. The simplest example occurs in a theory where the vacuum expectation value of a triplet higgs.
In fact, magnetic monopoles appear in spontaneously broken unified gauge theories even in the classical limit, as stable time independent solutions to the classical field equations. Pdf magneticmonopole excitations in the georgiglashow. Now the logic of the gauge principle, as usually presented, is the idea that the demand of local gauge covariance of ld in and of itself already leads to the. In these theories magnetic monopoles appear as topological solitons. The tevatron has inspired new interest in the subject of magnetic monopoles. We shall throughout take the gauge groupgto be su2 although our methods can in principle be extended to allg the data for a monopole on r 3 consist of a gauge field or connectiona. In the third section, we will introduce the fayetiliopoulos gauge invariance for this setup and show that it.
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