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Equations 1.1,1.2 are not unique. Suppose and , we
do not violate Maxwell's equations if
and
Typically one redefines
, returning the general gauge transform,

Two common gauges are the Coulomb and Lorenz. The Coulomb gauge has us take so that
.
Thus Equation 1.1 simplifies to a harmonic equation:
Unfortunately this does not do much to simplify the defining equation for the vector potential,
The Lorenz gauge has us chose
. Define the d'Alembertian
as
. Then the Lorenz gauge reduces the potential equations
to

** Next:** Quantization of an electromagnetic
** Up:** A Brief Introduction to
** Previous:** Potential Equations Maxwell's Equation.
Timothy Jones
2006-05-30