磁单极子存在时的Maxwell方程组的初边值问题

Initial-Boundary Value Problem for the Maxwell Equations When the Magnetic Monopole Is Exist

磁单极子的概念被狄拉克提出后,就一直被关注,但一直都没有发现其存在的证据,最近,一些物理学家在动量空间及自旋冰材料中找到其存在的确切证据.当磁单极子存在时,Maxwell方程就会发生变化.用复分析与四元数分析的方法,研究了磁单极子存在时的Maxwell方程组的初边值问题,获得了不同情况下问题的可解条件和通解.进一步完善用复分析与四元数分析的方法研究双曲型方程的边值问题的理论,并且对物理学中磁单极子存在时的电磁研究有一定的应用价值.

The magnetic monopole concept proposed by Dirac has been concerned, but there is still no evidence found to prove their existence. Recently, some physicists found the exact evidence in momentum space and spin ice materials. When magnetic mono- poles exist, the Maxwell equation will change. This paper investigates an initial-boundary value problem for the Maxwell equations when the magnetic monopole exists by using methods of complex analysis and quaternionic analysis to obtain the general solutions and solvable conditions to the problem respectively in different cases. This research can further improve the theory of study the boundary value problem for hyperbolic equations based on the complex analysis and four element analyses, moreover, it is applicable in the study of electromagnetic research in physics when magnetic monopoles exist.