Classical Electromagnetism and Special Relativity - Covariant Formulation in Vacuum

Covariant Formulation in Vacuum

The laws and mathematical objects in classical electromagnetism can be written in a form which is manifestly covariant. Here, this is only done so for vacuum (or for the microscopic Maxwell equations, not using macroscopic descriptions of materials such as electric permittivity), and uses SI units.

This section uses Einstein notation, including Einstein summation convention. See also Ricci calculus for a summary of tensor index notations, and raising and lowering indices for definition of superscript and subscript indices, and how to switch between them. The Minkowski metric tensor η here has metric signature (+−−−).