Internal structure of the monopoles

The non-abelian monopoles are shown to form linear multiplets under the color reflection symmetry of the original gauge group. This implies that as far as the gauge symmetry is kept unbroken only the singlet combinations of the monopoles may be admitted in the physical sector.     

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.     

Fundamental monopoles and multimonopole solutions for arbitrary simple gauge groups

Magnetic monopole solutions for an arbitrary compact simple gauge group are considered in the Prasad-Sommerfield limit. For each group and choice of symmetry breaking there is a set of fundamental monopoles with minimal topological charges and possessing no internal degrees of freedom; the number of these is less than or equal to the rank of the gauge group. It is shown that if the unbroken gauge group is abelian, all solutions with higher topological charges belong to p-parameter families, where p is the number of position and group orientation parameters needed to describe a set of non-interacting fundamental monopoles with the given topological charge. It is argued that these solutions, some examples of which are given, should therefore be interpreted as multimonopole configurations. An extension of these results to the case of a non-albelian unbroken gauge symmetry is conjecture and shown to be valid for a number of examples.     

Fermions and spherically symmetric monopoles

The interaction of fermions with monopoles is analyzed for general spherically symmetric monopoles of arbitrary strength and massless fermions in arbitrary representations of the gauge group. The results are based on a solution to the Dirac equation in the field of the monopole, valid in the point limit and in all partial waves. The partial waves in which non-conservation of global charges may occur are identified. A two-dimensional lagrangian is derived, which includes the Coulomb interactions generated by the complete abelian subgroup of the unbroken gauge group. The fermions are represented by a set of doublets with a boundary condition that reflects the structure of the core. We derive a simple formula for the conservation laws of this model which determine all scattering processes completely. The results have a consistent interpretation in terms of anomalies and field configurations with non-trivial winding number. We give an explicit construction of the zero modes for all helicity-violating multi-fermion condensates. The formalism is applied to several higher strength monopoles in SO(10) based models.     

Quark-confinement mechanism for SU(2) Yang–Mills theory in abelian gauge

By dimensional reduction in the sense of Parisi and Sourlas (PS), the gauge fixing term in the abelian gauge of the SU(2) Yang–Mills field is reduced to a two-dimensional O(3) nonlinear model. The confinement potential is obtained from magnetic monopoles and frame fluctuations. But the source of quark confinement is frame fluctuations and not magnetic monopoles. Because the frame cannot be regarded as a fixed one, the abelian projected SU(2) Yang–Mills field turns into a gauge field – one group element being with fixed frame , another group gauging the frame . The nonperturbative part becomes a dynamical gauge field in two dimensions, giving rise to the short range linear potential. Received: 4 September 2000 / Published online: 23 February 2001     

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.     

Nahm Transform for Periodic Monopoles¶and ?=2 Super Yang–Mills Theory

We study Bogomolny equations on ℝ²×?¹. Although they do not admit nontrivial finite-energy solutions, we show that there are interesting infinite-energy solutions with Higgs field growing logarithmically at infinity. We call these solutions periodic monopoles. Using the Nahm transform, we show that periodic monopoles are in one-to-one correspondence with solutions of Hitchin equations on a cylinder with Higgs field growing exponentially at infinity. The moduli spaces of periodic monopoles belong to a novel class of hyperk?hler manifolds and have applications to quantum gauge theory and string theory. For example, we show that the moduli space of k periodic monopoles provides the exact solution of ?=2 super Yang–Mills theory with gauge group SU(k) compactified on a circle of arbitrary radius. Received: 20 July 2000 / Accepted: 29 November 2000     

Evidence for monopoles in the quantizedSU(2) lattice vacuum: A study at finite temperature

InSU(2) gauge theory colour confinement occurs if the vacuum condenses into a coherent monopole plasma. To verify this picture, the first question to be answered is whether the vacuum supports monopoles at all. Since we expect the monopoles to be dilute and massive in the deconfinement, phase, we begin the search there. The method relies on cooling equilibrium lattice gauge field configurations—which are generated at the appropriate temperature—until the underlying semiclassical solutions emerge. We then pass to the confinement region and ask whether the monopoles condense. Finally, we repeat the procedure for gauge groupSU(3). The results confirm our expectations.     

Motion of test particles around monopoles

We present a detailed analysis of the motion of test particles around gauge and global monopoles using the Hamilton-Jacobi (HJ) formalism. We find that particles cannot be trapped by gauge monopoles while there may exist bound orbits for global monopoles under certain conditions.     

Massless monopoles and multi-pronged strings

We investigate the role of massless magnetic monopoles in the N=4 supersymmetric Yang-Mills Higgs theories. They can appear naturally in the 1/4-BPS dyonic configurations associated with multi-pronged string configurations. Massless magnetic monopoles can carry nonabelian electric charge when their associated gauge symmetry is unbroken. Surprisingly, massless monopoles can also appear even when the gauge symmetry is broken to abelian subgroups.     

规范场中单极子的某些研究

单极是规范场的一个内禀拓扑因素,而且单极的拓扑结构已足决定它的运动规律,这无论在阿贝尔或非阿贝尔场都如是。本文对规范场中单极子的基本概念作一个简单的介绍,并稍为涉及孤子单极,和单极在物理世界的可能存在问题。     

Three-Generat ion Models from Global Gauge Anomaly-Free Theories

In this work, we show how a global gauge anomaly of a gauge group H can be computed from a local one of a larger gauge group G ⊃ H. We also show that the number f of generations is tied to the consistency of a gauge theory H with initially a Z_f gIobal gauge anomaly. We give some examples of SU(N) models, in different dimensions of spacetime, with three families.     

Monopoles, instantons and chiral condensate in lattice QCD

We analyze the interplay of topological objects in four-dimensional QCD at finite temperature on the lattice. The distributions of color magnetic monopoles in the maximum abelian gauge are computed around instantons. Studies are performed in both pure and full QCD and in both the confinement and deconfinement phase. We find an enhanced probability for monopoles inside the core of an instanton on gauge field average. This is independent of the topological charge definition used. For specific gauge field configurations we visualize the situation graphically. Moreover the correlation of monopole loops and instantons with the chiral condensate is investigated. Strong evidence is found that clusters of the quark condensate and topological objects coexist locally on individual configurations.     

Magnetic monopoles, alive

We review recent developments in understanding the physics of the magnetic monopoles in unbroken non-Abelian gauge theories. Since numerical data on the monopoles are accumulated in lattice simulations, the continuum theory is understood as the limiting case of the lattice formulation. We emphasize physical effects related to the monopoles. In particular, we discuss the monopole-antimonopole potential at short and larger distances as well as a dual formulation of the gluodynamics, relevant to the physics of the confinement.     

Singular monopoles from Cheshire bows

Singular monopoles are nonabelian monopoles with prescribed Dirac-type singularities. All of them are delivered by Nahm's construction. In practice, however, the effectiveness of the latter is limited to the cases of one or two singularities. We present an alternative construction of singular monopoles formulated in terms of Cheshire bows. To illustrate the advantages of our bow construction we obtain an explicit expression for one U(2)$U(2)$ gauge group monopole with any given number of singularities of Dirac type.     

A NEW CO-BOUNDARY OPERATOR AND ITS APPLICATIONS

In this note new co-boundary operators are defined in the product form. The associative composition law of spatial translation group field is discussed using these new operators. The quantization condition of monopoles in SU(2) and SU(3) gauge theories follows easily from the new formalism.     

电磁学与电动力学中的磁单极-Ⅱ

本系列文章一共4篇,在电磁学和电动力学框架内用尽量科普的方式分别介绍磁单极的若干奇特性质.本篇文章主要介绍狄拉克磁单极是如何展示矢量势的规范变换的.我们首先简要介绍规范变换与规范对称性及狄拉克磁单极与狄拉克弦,然后讨论狄拉克磁单极与规范变换的联系.我们显式演示狄拉克弦摆动产生的规范变换,弦摆动区域对场点所张的立体角正比于规范变换的变换函数.磁偶极子则可以由两个无穷靠近的正反狄拉克磁单极构成.相应两条狄拉克弦位置的变化都对应磁偶极子矢量势的规范变换,特别当两条弦重合时弦效应相互抵消,只剩下纯的磁偶极子.传统的由磁偶极子产生的矢量势的规范变换则可以图像化为组成磁偶极子的正反狄拉克磁单极的狄拉克弦的摆动.我们显式地计算了位于坐标原点弦为直线的狄拉克磁单极,并进一步构造了没有奇异的吴大峻-杨振宁磁单极.     

Magnetic Monopoles and the Orientation Entanglement Relation

We show that Dirac magnetic monopoles do not satisfy the orientationentanglement (OE) relation and do not return to their initial state after a 4rotation. This is done in both the formalism using Dirac strings of singularitiesand in the fiber bundle formalism. In the latter we connect the OE relation tothe first homotopy group of the gauge group. We hypothesize that failure tosatisfy the OE relation is the reason Dirac magnetic monopoles have neverbeen seen.