Introduction to magnetic monopoles

One of the most basic properties of magnetism is that a magnet always has two poles, north and south, which cannot be separated into isolated poles, i.e. magnetic monopoles. There are strong theoretical arguments why magnetic monopoles should exist, but in spite of extensive searches they have never been found. This article gives an introduction to theoretical and experimental aspects of magnetic monopoles and discusses their role in our understanding of fundamental physics, both historically and today.     

Magnetic monopoles in gauge theories

Magnetic monopoles in gauge theories are investigated. Let G be the gauge group and H the group of symmetries which are not spontaneously broken. The existence of magnetic monopoles is proved in the case when the group G has a compact covering group but the covering group of H is non-compact.     

点电荷在拓扑绝缘体和导体中感应磁单极

利用电势和磁标势的第一类零阶贝塞尔函数的公式及拓扑绝缘体材料的本构关系, 推导了点电荷在电介质、 拓扑绝缘体和接地导体三个区域的感应电势及感应磁标势. 研究表明: 点电荷 在电介质、 拓扑绝缘体和接地导体中感应了像电荷和像磁单极; 感应像电荷和感应像磁单极的大小和正负除了与场源电荷、 拓扑绝缘体材料参数等因素有关外, 还与像电荷和像磁单极所处的空间位置有关.     

Hamiltonian nature of monopole dynamics

Classical electromagnetism with magnetic monopoles is not a Hamiltonian field theory because the Jacobi identity for the Poisson bracket fails. The Jacobi identity is recovered only if all of the species have the same ratio of electric to magnetic charge or if an electron and a monopole can never collide. Without the Jacobi identity, there are no local canonical coordinates or Lagrangian action principle. To build a quantum field of magnetic monopoles, we either must explain why the positions of electrons and monopoles can never coincide or we must resort to new quantization techniques.     

Magnetic monopoles and tachyons in special relativity

The mere special relativity does not explicitly predict existence of (sub-luminal) monopoles, but on the contrary explicitly predicts existence of super-luminal (tachyon) monopoles, with magnetic charge about 100 times less than usually assumed. This fact is relevant also at the light of current experiments looking for magnetic poles.     

Ratios of magnetic charge to charge and of magnetic mass to mass

It is shown that, unlike the case of (vacuum) solutions describing isolated bodies, conformal Killing fields are not excluded by the structure of vacuum gravitational magnetic monopoles at null infinity. The resulting dilation must be constant. This brings support to the viewpoint that such solutions might have a role to play in the understanding of gravitational entropy and time's arrow. If, in addition, a Maxwellian magnetic monopole (Dirac string singularity) is available, the ratio of the total magnetic charge (magnetic mass) over the total electric charge (mass) can be identified. This common feature between the gravitational and the electromagnetic interaction finds its origin in the space-time topology.     

Heavy and light monopoles in magnetic reversion in artificial spin ice

This work makes a theoretical study of the dynamics of emergent elemental excitations in artificial spin ice systems with hexagonal geometry during the magnetic reversion of the system. The magnetic and physical parameters of the nanoislands that form the array are considered as variables in the study. The parameters considered are: the energy barrier for the inversion of each nanoisland, the magnetic moment of the nanomagnets and the possible disorder in the sample. Our results show that the reversion dynamic presents two distinct mechanisms of magnetic reversion, with different elemental excitations for each mechanism. The first mechanism presents a reversion with the appearance of magnetic monopoles that do not move in the samples (heavy monopoles) and the absence of Dirac chains. In the other mechanism elemental magnetic excitations (light monopoles) appear that move great distances in the sample, giving rise to extensive Dirac chains during the magnetic reversion.     

Configurations of SO(3) monopoles with multiple magnetic charge

In this paper we consider configurations of monopoles with multiple magnetic charge in nonabelian gauge theory. Explicit gauge transformations are constructed which eliminate the string singularities for single monopoles of multiple magnetic charge, and for an arbitrary number of monopoles lying along a line. The question of finding nonsingular solutions is discussed.     

Branch Processes of Regular Magnetic Monopole

In this paper, by making use of Duan＇s topological current theory, the branch process of regular magnetic monopoles is discussed in detail. Regular magnetic monopoles are found generating or annihilating at the limit point and encountering, splitting, or merging at the bifurcation point and the degenerate point systematically of the vector order parameter field φ（x）. Furthermore, it is also shown that when regular magnetic monopoles split or merge at the degenerate point of field function φ, the total topological charges of the regular magnetic monopoles are stilI unchanged.     

Screening of the magnetic field by magnetic monopoles in spin ice

The screening of the external magnetic field by magnetic monopoles in spin ice has been considered. The polarization of the magnetic system with moving monopoles has been shown to result in the incomplete screening of the external magnetic field. The static permeability of spin ice and the magnetic-field screening length have been calculated and numerically estimated and the physical meaning of introducing monopoles is discussed.     

由正负磁单极对相互作用诱导的孤立狄拉克弦

基于三维旋量Gross-Pitaevskii(GP)方程研究在含时周期性外磁场作用下玻色-爱因斯坦凝聚体的动力学行为.结果显示,在含时周期外磁场的作用下,铁磁态自旋为1的玻色-爱因斯坦凝聚体将发生拓扑形变.当磁场的两个零点进入凝聚体后,自旋向上态的密度布居图在z轴上分别形成向上和向下的凸起.随着磁场的两个零点在凝聚体内逐渐重合,向上和向下的凸起被拉长,最终自旋向上态在z轴上呈线状分布,这与理论分析预测得到的孤立狄拉克弦相对应.最后,通过计算凝聚体的超流涡度给出磁单极的表征图.结果显示,凝聚体在磁场的两个零点处形成正、负磁单极对,分别对应着自旋向上态在z轴上向上和向下的凸起.随着磁场的两个零点重合,正、负磁单极对中的两条狄拉克弦逐渐靠近,之后大约经5 ms,它们完全相连,最终形成孤立的狄拉克弦.     

BPS two-monopole scattering

This work is a study of the classical interaction and behavior of two slowly moving, initially electrically netral BPS magnetic monopoles in a space free of other particles. In the scattering process, the monopoles are found to acquire equal and opposite electric charges, and the trajectories do not remain in the scattering plane, generically.     

Exact magnetic monopole solutions in Yang-Mills and unified gauge theories

We study the magnetic monopoles in non-Abelian gauge theories. The exact static, spherically symmetric solutions of the magnetic monopoles in both Yang-Mills and unified gauge theories are obtained. The energyE of the static system is calculable and it is either zero or infinite. The existence of the magnetic monopole solution is a consequence of symmetry rather than dynamics. We propose a new definition of the electromagnetic field tensor, which relates the static solution of gauge fields and the magnetic monopole solution. Experimental implications are discussed.     

Trapping energy of a magnetic monopole in magnetic materials

Analytical methods to investigate the interaction of magnetic monopoles with known magnetic media have been developed. Trapping energies of monopoles inside ferro-magnetic or super onducting materials of size greater than about 10⁻⁶ cm are found to be of the order of several kiloelectron volts. These are two to three orders of magnitude higher than in paramagnetic materials. Thus if stable magnetic monopoles exist at all in the universe, they are perhaps trapped in these magnetic materials. The effect of the finite size of the magnetic bodies is taken into account explicitly in our calculations of the trapping energy.     

Magnetic monopoles with Zn charges

Under some circumstances magnetic monopoles can be formed with charges which are additive modulo n. We speak of these as monopoles with Z_n charges. The conditions under which such monopoles arise are examined, and illustrated with some specific examples. These monopoles can be produced at intermediate stages of symmetry breakdown and converted at subsequent stages to ones with ordinary additive charges, specified by the group Z ≡ Z_∞. Simultaneously, new light monopoles with n times the Dirac charge can be produced. It is argued that such monopoles may be exempt from the most stringent cosmological bounds, and hence may be easiest to observe.     

The search for magnetic monopoles in magnetite from North China

Using the 27 kG magnetic field produced by a superconducting solenoid we have searched for trapped magnetic monopoles in a magnetite sample from North China. We hvve scanned the nuclear emulsion both for low ionizing tracks and heavily ionizing tracks, and polycarbonate track detectors for heavily ionizing tracks of magnetic monopoles. We obtained a 90% confidence level upper limit of 1.8×10⁻²⁶ monopoles per nucleon in the magnetite sample.     

Longitudinal plasma waves in the presence of monopoles of electron mass and electron charge

Dispersion relation for plasma waves in the presence of magnetic monopoles of electron mass and electron charge, is derived. It is shown that magnetic monopole charges, in general, dominate the dispersion. When monopoles form a fraction of the main body of plasma, there are two dominant oscillations. It is suggested that there can be electromagnetic emissions at these frequencies by nonlinear conversions. Possible application to the pulsar neighbourhood is envisaged.     

Interactions of magnetic monopoles with nuclei and atoms: Formation of bound states and phenomenological consequences

We discuss the binding of magnetic monopoles to nuclear and atomic systems. The energy spectrum is calculated, by assuming an interaction with a hard core. The formation process of monopole-nucleus bound states is analysed and it is shown that monopoles reaching Earth are most likely bound to a proton. We also discuss phenomenological implications of the existence of bound states in connection with the monopole catalysis of proton decay.