物理与工程

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.

These series include four individual papers,in which some peculiar properties of the magnetic monopole will be introduced as popular science in the frameworks of electromagnetism and electrodynamics.In this paper,we mainly discuss that how Dirac monopole exhibits the gauge transformation of a vector potential.Firstly,We give a brief introduction of gauge transformation,gauge symmetry,Dirac monopole,and Dirac string.Then we discuss the relation between Dirac magnetic monopole and gauge transformation.We explicitly show that the movement of Dirac string generates gauge transformation,and the solid angle faced by the region,where Dirac string sweeps up,is proportional to transformation function of the corresponding gauge transformation.Magnetic dipole can be made up from a pair of positive and negative Dirac monopoles.The changes of positions of the two corresponding Dirac strings are equivalent to the gauge transformations of the vector potential of the magnetic dipole.Specially,the effects of strings cancel each other when two Dirac strings coincide together,and a pure magnetic dipole is left.Traditional gauge transformation of a vector potential from a magnetic dipole now is pictured as the strings movement of corresponding Dirac monopoles.