Editing Magnetic vector potential (section)

== Electromagnetic four-potential ==
{{Main|Electromagnetic four-potential}}

In the context of [[special relativity]], it is natural to join the magnetic vector potential together with the (scalar) [[electric potential]] into the [[electromagnetic potential]], also called ''four-potential''.

One motivation for doing so is that the four-potential is a mathematical [[four-vector]]. Thus, using standard four-vector transformation rules, if the electric and magnetic potentials are known in one inertial reference frame, they can be simply calculated in any other inertial reference frame.

Another, related motivation is that the content of classical electromagnetism can be written in a concise and convenient form using the electromagnetic four potential, especially when the [[Lorenz gauge]] is used. In particular, in [[abstract index notation]], the set of [[Maxwell's equations]] (in the Lorenz gauge) may be written (in [[Gaussian units]]) as follows:
<math display="block">\begin{align}
  \partial^\nu A_\nu &= 0 \\
          \Box^2 A_\nu &= \frac{ 4\pi }{\ c\ }\ J_\nu
\end{align}</math>
where <math>\ \Box^2\ </math> is the [[d'Alembertian]] and <math>\ J\ </math> is the [[four-current]]. The first equation is the [[Lorenz gauge condition]] while the second contains Maxwell's equations.  The four-potential also plays a very important role in [[quantum electrodynamics]].