An Abelian gauge transformation changes by . Consequently gauge fixing by a quadratic function of retains transformations satisfying , subject to the same boundary conditions. Eliminating those residual transformations is part of specifying an inverse with a particular Green function prescription.
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The Lorenz gauge condition is a specific condition used in electromagnetism when working with the potentials of the electromagnetic fields. It is named after the physicist Ludvig Lorenz, who introduced it.