Abstract
The possibility of constructing a conformally invariant model of spinor quantum electrodynamics (QED) in four dimensions involving an anomalous dimension of the electron field and a general indecomposable conformal law for the Maxwell field Fµν is studied within the local indefinite metric framework making systematic use of conformal operator product expansions (OPEs). It is demonstrated that the standard elementary conformal law for Fµν, which is known to yield a vanishing current-current 2-point function leads to a trivial theory. On the other hand, the conformal invariant 2-point function <Jμ(x1)Jν(x2)> (proportional to the second order perturbation theory expression in a massless QED) gives rise to a soluble conformal model involving [Formula: see text] and a vector field Vµ with longitudinal correlation function. The question whether the model can be extended to include Fµν (rather than its divergence) remains unresolved.
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