Although this gauge is often erroneously attributed to the Dutch physicist H. A. Lorentz (Griffiths 1998), it was actually published by the Danish physicist L. Lorenz (Lorenz 1867, Whittaker 1989, van Bladel 1991). The magnetic and electric Fields are defined according to the vector potential A and the scalar potential by [rihgt](1)[/right] [rihgt](2)[/right] However, any constant can be added to and the gradient of any function can be added to A without changing the fields. The Lorenz gauge uses the Lorenz relation to simplify the wave equation. In cgs,
(3)
and in MKS
(4)
where is the permittivity of free space and is the permeability of free space.
Start with two of the Maxwell equations in MKS
(5)
to simplify the wave equation.
(6)
and
(7)
(8)
(9)
Plug the Lorenz relation into (6)
(10)
(11)
Now into (9)
(12)
(13)
(14)
Equations (11) and (14) can be written in one four-vector equation,
by
[rihgt](1)[/right]
[rihgt](2)[/right]
is the permittivity of free space and 
is the permeability of free space. 
