三种度规下Maxwell方程的双矢势对偶理论

Two Potential Duality Theory of Maxwell Equation under Three Metrics

介绍了电磁场双四维矢势的概念,讨论了三种度规下引入双矢势后电磁场张量的特性,给出了具有电磁对偶性的Maxwell方程。在有源情况下引入磁单极,利用电磁场的双矢势表述可以避开Dirac奇异弦得到具有电磁对偶性的电磁场方程。最后给出了有磁单极存在时具有SO(2)对称性的d'Alembert方程及推迟解。

In this paper, we introduce two 4-dimensional potentials for electromagnetic (EM) field, discuss the properties of EM tensor under three metrics, and then give out the EM duality symmetric Maxwell equations. In the case of existing source, we introduce magnetic monopole, and because we have two potentials expressions, we can obtain EM duality electromagnetic field equations without the concept of Dirac string. Finaly, we get the SO(2) symmetric d'Alembert equations and their retarded solutions in the presence of magnetic monopole.