130_notes.dvi

✷χ=−

[

∂Aν

∂xν

]

old

TheMaxwell equation with the Lorentz conditionnow reads

✷Aμ=−

jμ

c

.

There isstill substantial gauge freedompossible. The second derivative of Λ is set by the
Lorentz condition but there is still freedom in the first derivative which will modifyA. Gauge
transformations can be made as shown below.

Aμ→Aμ+

∂Λ

∂xμ

✷Λ = 0

This transformation will not disturb the Lorentz conditionwhich simplifies our equation.
We will use a further gauge condition in the next chapter to work withtransverse fields.