Gauge invariance and renormalization constants

Using only general considerations such as translation invariance, positive definite energy spectrum and gauge invariance, spectral representations have been set up for the vacuum expectation values of two photon and two electron operators in electrodynamics. The gauge dependence of such quantities is thus clearly exhibited, particularly that of equal time commutators and of propagators. Certain constants, related to the renormalization constants, integrals of the spectral functions are defined and shown to be gauge invariant. The generalized Ward identity is established in any gauge.