Theorem_lorentz_gauge_transformation.tex

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% Copyright © 2018 Peeter Joot.  All Rights Reserved.
% Licenced as described in the file LICENSE under the root directory of this GIT repository.
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\maketheorem{Lorentz gauge transformation.}{thm:gaugeTransformation:140}{
Given any multivector potential \( A \) solution of Maxwell's equation, the transformation
\begin{equation*}
A' = A - \stgrad \Psi,
\end{equation*}
where
\begin{equation*}
\dAlembertian \Psi = \gpgrade{ \conjstgrad A }{0,3},
\end{equation*}
allows Maxwell's equation to be written in wave equation form
\begin{equation*}
\dAlembertian A' = J.
\end{equation*}
A potential satisfying this wave equation is said to be in the \textit{Lorentz gauge}.
} % theorem