W.Thirring , H.Narnhofer Covariant QED without Indefinite Metric (41K, LaTeX) ABSTRACT. We construct for the linearized Higgs model a representation of the field operators in a Hilbert space H with the following features: 1) H has a positive definite metric but is nonseparable. 2) The vacuum is gauge invariant. 3) The gauge variant operators exist only in their exponentiated form as unitaries. 4) There is a subspace of H where $A_\mu{}^{,\mu}$ is represented by 0.