无限大平面磁通量的规律性及其应用

对于球解高对称性静磁场，如果仅应用安培环路定理和高斯定理，在解答中会存在一些不能唯一确定的常量，为了研究确定这些常量的规律，本讨论了穿过一个无限大平面的磁通量并用得到了一个有意义的结论。     

用高斯定理求电场的条件是满足环路定理

通过举例说明用高斯定理求电场的条件是:仅由对称性分析就能得出满足环路定理的电场形式.     

电磁学教学中对称性分析的积极意义

爱因斯坦狭义相对论的提出,导致对称性观念在物理学研究中占有重要地位,对称性要求对自然定律的形式是一条强有力的限制,对称性成为现代物理中的主角．阐述了对称性分析在电磁学教学中的积极意义。     

立体角概念在电磁学中的应用

用立体角概念和计算式导出高斯定律、安培环路定律，并举实例说明对具有一定对称性的静电场与稳恒磁场的场强分布可以较简捷地求解。     

安培环路定理的应用技巧

就如何判断问题是否满足条件∮L B·dl=BL进而可以用安培环路定理进行讨论．     

对称性在电磁场方向判断中的应用

在求解电磁场问题中,往往都需要判明总电场或磁场的方向,才好根据电场或磁场分布特点选取相应定理或定律来求解,分析常用的方法都是利用对称位置上取电荷元和电流元,再利用电磁场的叠加原理判断其方向.本文利用带电体和载流导体的对称性直接判断电场方向,分析过程更加简洁,不必涉及太多物理知识,这种分析方法对于初学电磁学的学生来说更加容易接受.     

含源轴对称轴外场的一种计算方法

利用高斯定理和环路定理及轴对称性,给出了由对称轴上的场计算含源轴外场的一种方法。     

电磁场的对称性分析

理工科大学生应该了解对称性的基本概念和做简单的对称性分析.我从1997年起在电磁学中结合环路定理和通量定理的应用来讲授这些内容,并写了两篇文章进行对称性分析的探讨[1,2].下面是经过不断改进后的有关教案,主要分电场和磁场两部分讨论.为减少篇幅,例题中与对称性无关的部分     

立体角概念在电磁学中的应用(续完)

用立体角概念和计算式导出高斯定律、安培环路定律，并举实例说明对具有一定对称性的静电场与恒定磁场的场强分布可以较简捷地求解。     

四元数在力学和电磁学中的应用

用双四元数表述了相对论力学和电磁规律,所用的方法能够适用于相对论性物理学科的不同领域,有利于形成系统的四元数物理学,由于四元数本身结构上的特点,使得四元数形式的物理量具备了反映四维时空中时间与空间内在联系的功能,从而用了数表述的相对论性物理学在一定程度上为揭示一些貌视无关的自然规律之间本质上的联系提供了可能性。     

The quantum poisson-Lie T-duality and mirror symmetry

Poisson-Lie T-duality in quantum N=2 superconformal Wess-Zumino-Novikov-Witten models is considered. The Poisson-Lie T-duality transformation rules of the super-Kac-Moody algebra currents are found from the conjecture that, as in the classical case, the quantum Poisson-Lie T-duality transformation is given by an automorphism which interchanges the isotropic subalgebras of the underlying Manin triple in one of the chirality sectors of the model. It is shown that quantum Poisson-Lie T-duality acts on the N=2 super-Virasoro algebra generators of the quantum models as a mirror symmetry acts: in one of the chirality sectors it is a trivial transformation while in another chirality sector it changes the sign of the U(1) current and interchanges the spin-3/2 currents. A generalization of Poisson-Lie T-duality for the quantum Kazama-Suzuki models is proposed. It is shown that quantum Poisson-Lie T-duality acts in these models as a mirror symmetry also. Zh. éksp. Teor. Fiz. 116, 11–25 (July 1999) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Quasiperiodic magnonic superlattices with mirror symmetry

We address the spin wave modes propagating in Fibonacci, Thue–Morse, and double period quasiperiodic magnonic superlattices. These structures are made of layers of a metamagnetic material alternating with layers of a nonmagnetic material, presenting mirror symmetry. Our calculations are carried out in the magnetostatic regime for the antiferromagnetic phase. Our model takes into account the presence of an external applied magnetic field, which is perpendicular to the interfaces of the superlattice, as well as the crystalline anisotropic contribution to the inner magnetic field. The magnetostatic bulk and surface modes are obtained by using the transfer matrix technique. The metamagnetic material considered here is FeBr₂, however, our results can be extended to other materials. Our numerical results show the behavior of these modes, for small frequencies of the energy spectra. The results reported here can be experimentally observed by light scattering techniques.     

GKZ-Generalized hypergeometric systems in mirror symmetry of Calabi-Yau hypersurfaces

We present a detailed study of the generalized hypergeometric system introduced by Gel'fand, Kapranov and Zelevinski (GKZ-hypergeometric system) in the context of toric geometry. GKZ systems arise naturally in the moduli theory of Calabi-Yau toric varieties, and play an important role in applications of the mirror symmetry. We find that the Gröbner basis for the so-called toric ideal determines a finite set of differential operators for the local solutions of the GKZ system. At the special point called the large radius limit, we find a close relationship between the principal parts of the operators in the GKZ system and the intersection ring of a toric variety. As applications, we analyze general three dimensional hypersurfaces of Fermat and non-Fermat types with Hodge numbers up toh ^1,1=3. We also find and analyze several non-Landau-Ginzburg models which are related to singular models.     

Natural electroweak breaking from a mirror symmetry

We present "twin Higgs models," simple realizations of the Higgs boson as a pseudo Goldstone boson that protect the weak scale from radiative corrections up to scales of order 5-10 TeV. In the ultraviolet these theories have a discrete symmetry which interchanges each standard model particle with a corresponding particle which transforms under a twin or a mirror standard model gauge group. In addition, the Higgs sector respects an approximate global symmetry. When this global symmetry is broken, the discrete symmetry tightly constrains the form of corrections to the pseudo Goldstone Higgs potential, allowing natural electroweak symmetry breaking. Precision electroweak constraints are satisfied by construction. These models demonstrate that, contrary to the conventional wisdom, stabilizing the weak scale does not require new light particles charged under the standard model gauge groups.     

Error compensation for mirror symmetry absolute test

A method is proposed to compensate intrinsic error in mirror symmetry absolute test. Because of the limitation of rotation times of flat A, intrinsic error of CNθ terms occurs in reconstructed wavefronts of flats A, B and C. If flat A is rotated to a new azimuthal position, and the wavefront difference between two measurements before and after rotation is calculated, the Zernike coefficients of CNθ terms can be obtained by solving coefficient equations due to rotation invariability of the form of Zernike polynomials in polar coordinates. Therefore, the intrinsic error of CNθ terms may be compensated. Because the amount of CNθ terms is infinite, the compensated terms are decided in terms of the balance between intrinsic error reduction and computational effort. Computer simulation proves the validity of the proposed method.     

Weak mirror symmetry of complex symplectic Lie algebras

A complex symplectic structure on a Lie algebra h$\mathfrak{h}$ is an integrable complex structure J$J$ with a closed non-degenerate (2,0)$(2,0)$-form. It is determined by J$J$ and the real part Ω$\Omega$ of the (2,0)$(2,0)$-form. Suppose that h$\mathfrak{h}$ is a semi-direct product g?V$\mathfrak{g}?V$, and both g$\mathfrak{g}$ and V$V$ are Lagrangian with respect to Ω$\Omega$ and totally real with respect to J$J$. This note shows that g?V$\mathfrak{g}?V$ is its own weak mirror image in the sense that the associated differential Gerstenhaber algebras controlling the extended deformations of Ω$\Omega$ and J$J$ are isomorphic.