norm). This is not the same thing as . Note that if O is any gauge invariant operator, does not depend upon the choice of the representatives of the equivalence classes, and so, this quantity is well-defined. This is not true for non-gauge-invariant operators in general because the Lorenz gauge still leaves residual gauge degrees of freedom. In an interacting theory of quantum electrodynamics, the Lorenz gauge condition still applies, but no longer satisfies the free wave equation. See also BRST formalism Quantum gauge theory Quantum electrodynamics ξ gauge Notes References Gauge theories Quantum electrodynamics