Master of Science
Department or Program
There is a topological structure in the set of the electromagnetic ﬁeld. The electromagnetic ﬁeld boundary-value problems are obtained as solutions to Maxwell’s equations, which are ﬁrst-order partial diﬀerential equations. This study will verify Maxwell’s equations in vacuum and have topological solutions characterized by the corresponding Hopf index n. Besides, this work will use the topological structure given by a scalar ﬁeld, which represents a map S 3 × R → S 2 and determines the electromagnetic ﬁeld through a certain transformation. We will show that the topological structure of the electromagnetic ﬁeld is due to Maxwell’s divergence conditions.