Editing Electromagnetic four-potential (section)

{{Use American English|date=March 2019}}{{Short description|Relativistic vector field}}
{{Electromagnetism|Covariance}}
An '''electromagnetic four-potential''' is a [[General relativity|relativistic]] [[vector function]] from which the [[electromagnetic field]] can be derived. It combines both an [[electric scalar potential]] and a [[magnetic vector potential]] into a single [[four-vector]].<ref>Gravitation, J.A. Wheeler, C. Misner, K.S. Thorne, W.H. Freeman & Co, 1973, {{ISBN|0-7167-0344-0}}</ref>

As measured in a given [[frame of reference]], and for a given [[Gauge theory|gauge]], the first component of the electromagnetic four-potential is conventionally taken to be the electric scalar potential, and the other three components make up the magnetic vector potential. While both the scalar and vector potential depend upon the frame, the electromagnetic four-potential is [[Lorentz covariance|Lorentz covariant]].

Like other potentials, many different electromagnetic four-potentials correspond to the same electromagnetic field, depending upon the choice of gauge.

This article uses [[tensor index notation]] and the [[Minkowski metric]] [[sign convention]] {{nowrap|(+ − − −)}}.  See also [[covariance and contravariance of vectors]] and [[raising and lowering indices]] for more details on notation. Formulae are given in [[International System of Units|SI units]] and [[Gaussian units|Gaussian-cgs units]].