Conformal invariant formulation of quantum electrodynamics

A self-consistent version of conformal-invariant quantum electrodynamics is formulated. Explicit expressions are constructed for three-point Green's functions including the electromagnetic vector potential and the current. These Green's functions are different from the usual conformal-invariant expressions. The difference is due to the absence of decomposition for representations the conformal group corresponding to the potential and the current. A proof is presented that the skeleton perturbation theory constructed with such modified Green's functions is conformal-invariant. It is shown that in the conformal-invariant theory the Maxwell equations in the Euclidean space arise from the requirement of (partial) equivalence of representations corresponding to the fields Asub(μ), Fsub(μν) and jsub(μ)