Solution of the Dirac equation by separation of variables in spherical coordinates for a large class of non-central electromagnetic potentials

A systematic and intuitive approach for the separation of variables of the three-dimensional Dirac equation in spherical coordinates is presented. Using this approach, we consider coupling of the Dirac spinor to electromagnetic four-vector potential that satisfies the Lorentz gauge. The space components of the potential have angular (non-central) dependence such that the Dirac equation becomes separable in all coordinates. We obtain exact solutions for a class of three-parameter static electromagnetic potential whose time component is the Coulomb potential. The relativistic energy spectrum and corresponding spinor wave functions are obtained. The Aharonov–Bohm and magnetic monopole potentials are included in these solutions.     

Algebra with polynomial commutation relations for the Zeeman effect in the Coulomb-Dirac field

We consider a model of particle motion in the field of an electromagnetic monopole (in the Coulomb-Dirac field) perturbed by homogeneous and inhomogeneous electric fields. After quantum averaging, we obtain an integrable system whose Hamiltonian can be expressed in terms of the generators of an algebra with polynomial commutation relations. We construct the irreducible representations of this algebra and its hypergeometric coherent states. We use these states to represent the eigenfunctions of the original problem in terms of the solutions of the model ordinary differential equation. We also present the asymptotic approximations of the eigenvalues in the leading term of the perturbation theory, where the degeneration of the spectrum is removed completely.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 1, pp. 127–147, January, 2005.     

On the interbasis expansion for the Kaluza-Klein monopole system

We study the interbasis expansion of the wave-functions of the Kaluza-Klein monopole system in the parabolic coordinate system with respect to the spherical coordinate system, and vice versa. We show that the coefficients of the expansion are proportional to Clebsch-Gordan coefficients. We analyse the discrete and continuous spectrum as well, briefly discuss the feature that the (reduced) Kaluza-Klein monopole system is separable in three coordinate systems, and the fact that there are five functionally independent integrals of motion, respectively observables, a property which characterizes this system as super-integrable.     

On the classical solution of SO(3) gauge theory and ’t Hooft-Polyakov monopole

It is shown that the ansatz for the asymptotic (r → ∞) gauge fields used by ’t Hooft in the study of monopoles in SO(3) electroweak theory is not unique.     

磁单极子进展概述

自磁单极子概念被狄拉克提出以来,不管是理论还是实验物理学家都一直在努力寻找,但迄今仍然没能找到它们存在的确凿证据.最近,一些凝聚态物理学家声称在动量空间以及自旋冰材料中找到了磁单极子存在的有力证据,并通过磁单极子的集体激发行为解释了一些新颖的物理现象.这使得磁单极子艰难的探索之路出现了一丝新的曙光.作为电动力学教学内容的补充,本文拟把磁单极子的最新进展做一个概述,让大学生对此有一个全面的认识,从而激发他们学习和科研的兴趣.     

Orbits in the field of a gravitating magnetic monopole

Orbits of test particles and light rays are an important tool to study the properties of space-time metrics. Here we systematically study the properties of the gravitational field of a globally regular magnetic monopole in terms of the geodesics of test particles and light. The gravitational field depends on two dimensionless parameters, defined as ratios of the characteristic mass scales present. For critical values of these parameters the resulting metric coefficients develop a singular behavior, which has profound influence on the properties of the resulting space-time and which is clearly reflected in the orbits of the test particles and light rays.     

Affine A3^（1） N = 2 Monopole as the D Module and AiTine ADHMN Sheaf

A Higgs-Yang-Mills monopole scattering spherical symmetrically along light cones is given. The left incoming anti-self-dual α plane fields are holomorphic, but the right outgoing SD β plane fields are antiholomorphic, meanwhile the diffeomorphism symmetry is preserved with mutual inverse afiine rapidity parameters μ and μ^-1. The Dirac wave function scattering in this background also factorized respectively into the （anti）holomorphic amplitudes. The holomorphic anomaly is realized by the center term of a quasi Hopf algebra corresponding to an integrable conformal affine massive field. We find explicit Nahm transformation matrix （Fourier Mukai transformation） between the Higgs YM BPS （fiat） bundles （1） modules） and the affinized blow up ADHMN twistors （perverse sheafs）. Thus we establish the algebra for the ＇t Hooft Hecke operators in the Hecke correspondence of the geometric Langlands program.     

三维FW-H方程与CAA数值模拟匹配技术研究

本文研究了三维FW-H方程与CAA数值模拟匹配技术。首先验证了适于亚音任意运动声源的Farassat时域公式和适于亚音匀速直线运动声源的Lockard频域公式,采用均匀流中单极子源声辐射问题对两类公式进行了校核。进一步,采用FW-H／CAA匹配技术对风扇／压气机前传声进行了预测。近声场基于轴对称三维CAA方法获得,远声场则基于近声场数据采用三维可穿透FW-H方程时域公式进行预测,并校核算例着重分析了不同积分面对远场声指向性的影响。本文研究证实了FW-H／CAA数值模拟匹配技术的可行性和解决工程实际问题的潜力。     

Nuclear Structure and Electromagnetic Transitions Investigation in Er Isotopes within Framework of Interacting Boson Model

Interacting Boson Model-2 (IBM-2) is used to determine the Hamiltonian for Er nuclei. Fit values of parameters are used to construct the Hamiltonian, energy levels and electromagnetic transitions (B(E2), B(M1)) multipole mixing ratios (δ(E2/M1)) for some even-even Er nuclei and monopole transition probability are estimated. New ideas are used for counting bosons number at N = 64 and results are compared with previous works.