不可易规范场的对偶荷

本文讨论了不可易SU(2)规范场的各种规范不变物理量——电荷、对偶荷(磁荷)、电磁场以及有质量矢粒子场的表达式与关系,特别是对偶荷(磁荷)与电荷算符同位旋方向的大范围拓扑性质的关系。     

弯曲空间的SU(N)规范理论的磁单极子与双子解

(一) 自′t Hooft得到SU(2)规范场的经典磁单极子解以来,在弯曲空间中的SU(2)规范场的解也有了一系列的研究,结果表明静态中心球对称解的弯曲空间度规与U(1)场的Reissner-Nordstrom度规相同,只不过把e~2换成SU(2)的规范荷Q~2与其对偶荷(磁荷)g_(2)~2的平方和O~2+g_(2)~2.Yasskin较普遍地研究了Einstein-Yang-Mills场耦合方程的求解问题,提出它们可由弯曲空间电磁场的解来构成.但构成时引入的参量β~p的意义不明确.     

SU(4)磁单极子与双子解

以SU(4)规范群为例,提出一个简单求解磁单极子及双子的经典解的方法,它可系统地推广于一般的SU(N)群的情况.所得到的SU(4)单磁荷为■     

读“等效的磁荷观点”有感

文章在假想的“磁荷世界”中修改了麦克斯韦方程组和洛伦兹力公式.由磁的库仑定律出发,并根据磁荷与电荷产生的电磁场的等效性,得到真空中静磁场的高斯定理和环路定理.仿照“电荷世界”中的电流定义了磁流强度,又根据磁场的相对论变换,由毕奥—萨伐尔定律和法拉第电磁感应定律得到稳恒电场D的高斯定理和环路定理.     

关于SU(2)规范场的结构

最近,吴大峻、杨振宁发现在Abel的U(1)规范场的情况下,磁荷的量子化数值与纤维丛的示性数相对应。但是在SU(2)规范场的情况下,由于球面上的SU(2)丛只有一种类型,于是必须寻找另外的拓扑不变关系,用它的特征类来区分具有不同单磁极的规范场。在文献[2]中我们曾注意到单磁极与SU(2)规范场的电荷算符的同位旋方向的拓扑关系,本文进一步结合SU(2)纤维丛及其U(1)子丛的关系,研究SU(2)规范场的分类。     

SU(2)规范场的一系列“无源”解——静点磁荷系的SU(2)势及U(1)势

场与源这一对矛盾双方如何对立与统一是经典电磁场及引力场理论中议论纷云的一个根本问题.非Abel规范场的静无源解(应该说是无外源,但以场自身为源)提供了一个不含奇异点的、场与源互相制约构成自洽稳定的有机统一体的一个值得注意的例子(孤粒子).现有的这种解都是在无外源(实际上以场的奇异点——磁荷为源)的吴杨单位磁荷解([4]的情况a)的基础上加上径向“形状因子”得到的,因此只限于总磁荷为单位值(本文取Schwinger量子化值为磁荷单位)的静同步球对称情况.为了弄清楚更一般     

磁荷对中子星质量半径比的约束

讨论了荷电(磁)质点的量子力学波方程及其解. 由磁场中解的奇异性讨论了磁单极的存在; 由Rubakov-Callan模型推知中子星可能含有大量磁单极. 然后采用中子星的结构方程, 讨论了磁荷对中子星质量半径比的约束, 分别得到了磁荷对中子星质量半径比上限的影响 和磁荷对中子星质量半径比下限的影响的数学表达式. 关键词： 磁单极 中子星 质量半径比     

孤立磁极存在吗?

孤立的正、负电荷是存在的。那么孤立的南、北磁荷是否也可能存在呢?通常电磁场方程组在形式上的不对称是否表明人们对电磁现象实质的认识还有某些片面性呢? 一、单磁子存在假设 1931年,狄拉克(Dirac)首先指出[1]:量子力学并不排斥单磁极[以下简称单磁子(monopole)]的存在。而且单磁极的磁荷g与电子电荷e之间有下面的关系:[后来施温格(Schwinger)再次探讨了这个问题[2],他认为这个关系应是:若将n=1时的g记作V。,便有 。P。。-=h(2) 2这就是基本电荷;与基本单磁子磁荷仁。之间的关系.由此式可以估计,p。一1卜竺。3.3x10-·电磁单位. -——-…     

双荷静止球对称天体Einstein—Maxwll方程的共形平直内解

严格解出一种既荷电又荷磁，且电荷密度与磁荷密度之比为常量的静止球对称天体的共形内解。     

关于相对论量子力学中某些相角不定性的消除

在量子力学的某些问题中,常常存在相角的不定性.最近在研究不动的电中性磁荷与荷电Dirac粒子的散射问题中,风间洋一、杨振宁和Goldhaber为了消除相角不定性,引入了附加磁矩.本文不引入附加磁矩,而利用文章中所建议的调整了的量子力学框架、正交判据和能量的变分原则(不定相角作为变分参数)唯一地确定了相角、散射截面和束缚态.由于结果与[2]的一致,使这些定解原则受到一次检验.利用这些定解原则,解决了荷电磁荷与荷电Dirac粒子及正负磁荷对偶的散射态和束缚态等问题.     

ON THE ELIMINATION OF PHASE ANGLE UNCERTAINTY IN SOME PROBLEMS OF RELATIVISTIC QUANTUM MECHANICS

In some quantum mechanical problems involving singular states usually exists phase angle uncertainty. Recently in the investigation of the scattering of a Dirac particle with the charge Ze and a fixed magnetic monopole, Kazama, Yang and Goldharber [2] introduced some extra magnetic moments in order to eliminate the phase angle uncertainty. In this paper, instead of introducing any extra magnetic moment we use the adjusted framework of quantum mechanics suggested in [3], the criterion of orthogonality and the variation principle of energy (indefinite phase as a variation parameter) to determine the phase angle, the scattering cross section and the bound states uniquely. These principles for the determination of the solution have been tested for its correctness, because the result is consistent with the solution of reference [2]. By using these principles the problems of scattering and bound states of systems consisting of a charged magnetic monopole and a charged Dirac particle, as well as the monopole pair are exactly solved.     

THE MULTISYNCHRO-SPHERICAL SOLUTIONS OF THE SU(N)GAUGE THEORY

We study the monopole solutions of the SU(N) gauge group systematically,generalize the current synchro-spherical symmetrical monopole to the multi synchro-spherical symmetrical case,and give the complete classification of the monopole so-lutions.As examples,we have calculated the SU(3) and SU(4) monopoles in detail,and discuss some problems such as angular momenta and topological quantum num-bers.     

Cyclic Monopoles,Affine Toda and Spectral Curves

We show that any cyclically symmetric monopole is gauge equivalent to Nahm data given by Sutcliffe’s ansatz, and so obtained from the affine Toda equations. Further the direction (the Ercolani-Sinha vector) and base point of the linearising flow in the Jacobian of the spectral curve associated to the Nahm equations arise as pull-backs of Toda data. A theorem of Accola and Fay then means that the theta-functions arising in the solution of the monopole problem reduce to the theta-functions of Toda.     

A Gauge Theoretical View of the Charge Concept in Einstein Gravity

We will discuss some analogies between internal gauge theories and gravity in order to better understand the charge concept in gravity. A dimensional analysis of gauge theories in general and a strict definition of elementary, monopole, and topological charges are applied to electromagnetism and to teleparallelism, a gauge theoretical formulation of Einstein gravity. As a result we inevitably find that the gravitational coupling constant has dimension /l ², the mass parameter of a particle dimension /l, and the Schwarzschild mass parameter dimension l (where l means length). These dimensions confirm the meaning of mass as elementary and as monopole charge of the translation group, respectively. In detail, we find that the Schwarzschild mass parameter is a quasi–electric monopole charge of the time translation whereas the NUT parameter is a quasi–magnetic monopole charge of the time translation as well as a topological charge. The Kerr parameter and the electric and magnetic charges are interpreted similarly. We conclude that each elementary charge of a Casimir operator of the gauge group is the source of a (quasi-electric) monopole charge of the respective Killing vector.     

Topological extensions of Noether charge algebras carried by Dp-branes

We derive an extension of the supersymmetry algebra carried by D-branes in a massless type IIA superspace vacuum. We find that the extended algebra contains not only topological charges that probe the presence of compact space-time dimensions but also pieces that measure non-trivial configurations of the gauge field on the world-volume of the brane. Furthermore there are terms that measure the coupling of the non-triviality of the world-volume regarded as a U(1) bundle of the gauge field to possible compact space-time dimensions. In particular, the extended algebra carried by the D2-brane can contain the charge of a Dirac monopole of the gauge field. In the course of this work we derive a set of generalized Gamma-matrix identities that include the ones presently known for the IIA case. In the first part of the paper we give an introduction to the basic notions of Noether current algebras and charge algebras; furthermore we find a theorem that describes in a general context how the presence of a gauge field on the world-volume of an embedded object transforming under the symmetry group on the target space alters the algebra of the Noether charges, which otherwise would be the same as the algebra of the symmetry group. This is a phenomenon recently found by Sorokin and Townsend in the case of the N15-brane, but here we show that it holds quite generally, and in particular also in the case of D-branes.     

On the structure of generalized monopole solutions in gauge theories

A method is presented for constructing generalized 't Hooft monopole solutions in a gauge theory with an arbitrary gauge group. We derive restriction arising from the condition of finite energy. The radial oscillation of the solution is discussed. Using our method we reproduce all the SU(3) solutions known in the literature. Finite energy monopoles possessing magnetic charge in the range g₀?kg₀?(N?1)g₀ are found in SU(N) gauge theories. Different charge quantization conditions are analyzed to understand the structure of our solutions.     

A ring of instantons inducing a monopole loop

We consider the superposition of infinitely many instantons on a circle in . The construction yields a self-dual solution of the Yang-Mills equations with action density concentrated on the ring. We show that this configuration is reducible in which case magnetic charge can be defined in a gauge invariant way. Indeed, we find a unit charge monopole (worldline) on the ring. This is an analytic example of the correlation between monopoles and action/topological density, however with infinite action. We show that both the Maximal Abelian Gauge and the Laplacian Abelian Gauge detect the monopole, while the Polyakov gauge does not. We discuss the implications of this configuration.     

ON THE ENERGY LEVELS AND THE STATIONARY STATES OF THE EXOTIC ATOMS CONTAINING MONOPOLES

In this short paper, which is based on an analysis of some contradictions of the principles for the determination of the solution in usual quantum mechanics, and we suggest an adjusted framework of quantum mechanics, which naturally contains essentailly singular states. By using the monopole harmonics, which were studied by Yang and Wu, we solve the stationary state problems of the exotic atoms, which contain the magnetic monopole and different elementary particles.     

Introduction to Jebsen's paper

Brief comment on a 1921 paper by Jebsen.This work provides the first published proof of “Birkhoff's” theorem. The author, who seems to have been an undergraduate at the time (tragically, he died shortly afterwards) understood (as did many others) that Einstein's equations reduced considerably in a “minimal,” namely two-component, metric in a simple gauge such as Schwarzschild's; a good part of the paper is devoted to deriving this interval form.The originality of his work lies instead in showing that time-independence of the exterior Schwarzschild solution need not be assumed, but is a consequence of Einstein's equations.From a modern perspective, it is a bit surprising that this result was not found earlier: for example, Einstein studied the spherical solution in the linearized theory, whose kinship to Maxwell's might have suggested the obvious parallel to charge conservation. In current language, the theorem states gauge theories forbid monopole radiation because they have no helicity zero modes.Editor's note: Further references to early derivations of “Birkhoff's” theorem can be found in [1] and [2] while [3] is one of the few papers that calls it “Jebsen-Birkhoff.” Since few's was written a more detailed biography of Jebsen has now appeared: gr-qc/0508163, by Johausen &; Ravulal. Work supported by NSF Grant PHY04-00609     

Cylindrically and spherically symmetric monopoles in SU(3) gauge theory

We apply to the Atiyah-Ward ansätze a systematic procedure locating symmetric monopoles in SU(3) gauge theory broken to U(1) × U(1). In particular we recover the known spherically symmetric monopole as a limit of a cylindrically symmetric separated two monopole solution in SU(3). We also discuss the spherically symmetric monopole in SU(n). This latter is the only instance where we have properly shown the smoothness of the Higgs and gauge fields.