Maxwell equations and direction of electromagnetic field

R. Ya. Nizkii

Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 9, Tome 329 (2005), pp. 118-146

Résumé

A mapping $F\colon U\to\Lambda_2(M_0)$, $U\subset\mathbb R^4$, satisfying the Maxwell equations is regarded as the tensor of a certain electromagnetic field (EM-field) in vacuum. The EM-field is described on the basis of a special decomposition $F=e\omega+h(\ast\omega)$, where the mapping $\omega\colon U\to G^1$ is called the direction of the EM-field, and $e\colon U\to (0,+\infty)$ and $h\colon U\to\mathbb R$ are the electric and magnetic coefficients of the EM-field. The Maxwell equations are reformulated in terms of $\omega$, $e$, and $h$. EM-fields whose set of directions is a point or a one-dimensional subset of $G^1$ are considered.