Riemann–Silberstein vector

In mathematical physics, in particular electromagnetism, the Riemann–Silberstein vector, named after Bernhard Riemann and Ludwik Silberstein, (or sometimes ambiguously called the "electromagnetic field") is a complex vector that combines the electric field E and the magnetic field B.

Given an electric field E and a magnetic field B defined on a common region of spacetime, the Riemann–Silberstein vector is

where c is the speed of light, with some authors preferring to multiply the right hand side by an overall constant ${\displaystyle {\sqrt {\epsilon _{0}/2}}}$ where ε₀ is the permittivity of free space. It is analogous to the electromagnetic tensor F, a 2-vector used in the covariant formulation of classical electromagnetism.

In Silberstein's formulation, i was defined as the imaginary unit, and F was defined as a complexified 3-dimensional vector field. The value of F at an event was a bivector.

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