A New Covariant Auxiliary Condition for Quantum Electrodynamics

The covariant auxiliary condition Eq. (3) or (15) is assumed to be valid for all states occurring in nature. Such special assumptions as the condition for a "photon vacuum" of the type of the noncovariant Eq. (18) then become superfluous. The meaning of the new auxiliary condition (15) is that the expectation value of the electromagnetic field is equal to that of the retarded field from charged matter: "All light has once been emitted." If in some discussion of properties of a particular photon one wants to ignore the source of that particular photon (without denying its existence), one can ignore Eqs. (3) and (15) in such a special case, replacing them by an appropriate "practical" boundary condition. In self-energy calculations one sometimes uses a "photon vacuum" condition of the type of Eq. (20). Such approximation to (15) gives correct results up to second but not to fourth powers of $e$.