Monopole charges for arbitrary compact gauge groups and Higgs fields in any representation

The topological invariants of monopoles are described for an arbitrary compact gauge groupG and Higgs field in any representation. The results generalize those obtained recently for compact and simply connectedG and in the adjoint representation. The cases when the residual symmetry group isH=U(1) orH=U(3) are worked out explicitly. This latter is needed to accommodate fractional electric charge with monopoles having one Dirac unit magnetic charge.The general theory is illustrated on the SU(5) monopole.     

The four states of the Massless neutrino with pauli coupling by Spin-Gauge invariance

The Pauli coupling is introduced for four-component neutrino states and related to local T ⁴SU(2,2) spin-gauge (not internal symmetry) transformations applied to the massless Dirac equation. The well-known left-right asymmetry for free neutrino helicity states is generalised and discussed for Pauli-coupled neutrinos. An explicit exact solution is obtained for Pauli-coupled neutrino equations in an external free radiation field by the use of the above local spin-gauge transformations. It is also suggested that local SL(2, C)SU(2,2) spin-gauge transformations can be used to obtain models of neutral currents for neutrinos.     

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.     

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.     

O(5)×U(1) electroweak gauge theory and the neutrino oscillations in matter

A study is made of the groupO(5)×U(1). The group is economical in the number of gauge bosons, which we associate with each of its generators, and is anomaly-free. The left-handed leptonsL _L ^T (v _e ,e,,v ) _L are assigned to the four-dimensional spinorial representations ofO(5). The right-handed particles are taken to be the singlets of the group. The theory has three sets of gauge bosons: (1) analogues of the GWS model, (2) additional charged gauge bosons, and (3) a set of three additional neutral gauge bosons as compared to the GWS model. We introduce neutrino mixing by mixing the additional charged gauge bosons. We develope a theory of neutrino oscillations in matter in such a way that in the absence of matter the scattering length reduces to the usual scattering length in vacuum. Even if the neutrino masses are equal or the neutrinos are massless, we still have neutrino oscillations in matter, a result already noted by Wolfenstein.     

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.     

Coulomb scattering of an electron by a monopole

The Coulomb scattering of an electron by a magnetic monopole is analyzed using a lowest-order quantum perturbation approximation suggested by a two-potential Lagrangian form for classical electromagnetism, generalized through the use of spacetime algebra to include magnetic monopoles. Good agreement with existing conventional analyses of this problem is demonstrated.1. Work supported by Department of Energy contract DE-AC03-76SF00515.2. The idea to employ spacetime algebra (sometimes called Dirac algebra) to incorporate magnetic monopoles into classical electromagnetic theory was proposed by de Faria-Rosaet al. [3].3. This is a factori difference between the definition of 5 by Eq. (3) and that by Bjorken and Drell [6]. Since a cross section (without interference terms) is being calculated, we can ignore this distinction.     

Dirac-Yang monopoles in all dimensions and their regular counterparts

The Dirac-Yang monopoles are singular Yang-Mills field configurations in all Euclidean dimensions. The regular counterpart of the Dirac monopole in D = 3 is the’ t Hooft-Polyakov monopole, the former being simply a gauge transform of the asymptotic fields of the latter. Here, regular counterparts of Dirac-Yang monopoles in all dimensions are described. In the first part of this work, the hierarchy of Dirac-Yang monopoles will be defined; in the second part, the motivation to study these in a topical context will be briefly presented; and in the last part, two classes of regular counterparts to the Dirac-Yang hierarchy will be presented. The text was submitted by the author in English.     

统一场论中的磁单极

本文的主要目的是介绍磁单极理论的基本结果。 我们首先介绍Dirac磁单极的基本思想。然后,进一步评述统一场论中的拓扑磁单极,并说明磁单极在早期宇宙中是怎种产生的。最后,我们讨论磁单极问题上最惊人的现象——磁单极对核子衰变的催衰化作用及其温度依赖关系。     

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.     

Monopoles without strings: a conflict between the one-photon condition and duality invariance

We prove a new no-go theorem in the Dirac-algebra formulation of generalized electromagnetic theory, which includes magnetic monopoles and uses two potentialsA andM : It is impossible to construct a Lagrangian which is duality invariant and satisfies the one-photon assumption, from which Maxwell's equations and the equations of motion can be derived. Such a Lagrangian can be found only if either duality invariance or the one-photon assumption is sacrificed. These constraints as well as others discussed here are based on recently published results on monopoles without strings in the Dirac algebra, but they do not arise from any artificial restrictions in the Dirac-algebra formulation.     

Lepton flavour symmetry and the neutrino magnetic moment

With the standard model gauge group and the three standard left-handed Weyl neutrinos, two minimal scenarios are investigated where an arbitrary non-Abelian lepton flavour symmetry groupG _H is responsible for a light neutrino with a large magnetic moment. In the first case, with scalar fields carrying lepton flavour, some finetuning is necessary to get a small enough neutrino mass for _v =O(10)^–11 _B. In the second scenario, the introduction of heavy charged gauge singlet fermions with lepton flavour allows for a strictly massless neutrino to one-loop order. In both cases, the interference mechanism for smallm and large _v is unique, independently ofG _H . In explicit realizations of the two scenarios, the horizontal groups are found to be non-Abelian extensions of a Zeldovich-Konopinski-Mahmoud lepton number symmetry. Only a discrete part ofG _H is spontaneously broken leading to a light Dirac neutrino with a large magnetic moment.     

Universal Spin Structure

Any Dirac spin structure on a world manifold xis a subbundle of the composite spinor bundle , where is a bundle oftetrad gravitational fields. The bundle S admits generalcovariant transformations that enable us to discover theenergy-momentum conservation law in gauge gravitationtheory.     

Topological electric charge

By treating magnetic charge as a gauge symmetry through the introduction of a magnetic pseudo four-vector potential, we show that it is possible to construct a topological electric charge from a theory which originally contains gauge magnetic charge. This is an explicit realization of the Montonen-Olive conjecture that there should exist a dual theory to the usual 't Hooft-Polyakov monopole theory in which the roles of the gauge and topological charges are reversed. The physical distinction between 't Hooft-Polyakov monopoles and the dual theory with electric charge is that the strong and weak coupling regimes are reversed. Physically this leads to the mass of the electrically charged soliton being on the order of (1/137)M _W as opposed to the much larger mass (on the order of 137M _W) of the magnetically charged soliton. Thus even forM _W in the TeV range such an electrically charged particle could be observed at some future accelerator.     

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.     

Chiral (γ5) symmetry of massless fields and neutrino theory of photons

It is shown that the field theory of massless particles has the internal symmetry groupG=U(1) AutU(1). The ₅ and dual transformations of neutrino and electromagnetic fields are particular cases of the transformations of this group. TheCP transformations of massless field can also be included in the transformations of this group. The following formulation of Pryce (1938) theorem is given: Statistical properties of the composite photon in the neutrino theory of light are inconsistent with chiral (₅) symmetry of neutrino and electromagnetic fields.     

Topological aspects of Yang-Mills theory

The space of mapsS ³ G has components which give the topological quantum number of Yang-Mills theory for the groupG. Each component of the space has further topological invariants. WhenG=SU(2) we show that these invariants (the homology groups) are captured by the space of instantons. Using these invariants we show that potentials must exist for which the massless Dirac equation (in Euclidean 4-space) has arbitrarily many independent solutions (for fixed instanton number).     

Maxwell electrodynamics from a theory of macroscopically extended particles

It is shown that an approach to quantum phenomena in which charged particles are treated as macroscopically extended periodic disturbances in a nonlinear c-number field, interacting with each other via massless excitations of that field, leads almost uniquely to the five basic equations of classical electrodynamics: the Lorentz force law and Maxwell's equations. The fundamental electromagnetic quantity in this approach is the 4-vector potential A—interpreted absolutely as a measure of the local shift of each particle off its mass shell—rather than theE andB fields, and it thus provides a new viewpoint on the questions of Aharonov-Bohm phase shifts, the existence of magnetic monopoles, and the role of gauge invariance.     

Neutrino Mass Generation in SO(4) Model

Generation of neutrino mass in SO(4) model is proposed here. Thealgebraic structure of SO(4) is same as to that of SU(2)_L ×SU(2)_R. It is shown that the spontaneous symmetry breaking results three massive as well as three massless gauge bosons. The standard model theory according to which there exist three massive gauge bosons and a massless one is emergedfrom this model. In the framework of SU(2)_L × SU(2)_R a small Dirac neutrino mass is derived. It is also shown that such mass term may vanish with a special choice. The Majorana mass term is not considered here and thus in this model the neutrino mass does not follow seesaw structure.