97 12 04 5 v 1 4 D ec 1 99 7 Conformally Invariant Green Functions of Current and Energy - Momentum Tensor in Spaces of Even Dimension D ≥ 4

We study the conformally invariant quantum field theory in spaces of even dimension D ≥ 4. The conformal transformations of current j µ and energy-momentum tensor T µν are examined. It is shown that the set of conformal transformations of particular kind corresponds to the canonical (unlike anomalous) dimensions l j = D − 1 and l T = D of those fields. These transformations cannot be derived by a smooth transiton from anomalous dimensions. The structure of representations of the conformal group, which correspond to these canonical dimensions, is analyzed, and new expressions for the propagators j µ j ν and T µν T ρσ are derived. The latter expressions have integrable singu-larities. It is shown that both propagators satisfy non-trivial Ward identities. The higher Green functions of the fields j µ and T µν are considered. The confor-mal QED and linear conformal gravity are discussed. We obtain the expressions for invariant propagators of electromagnetic and gravitational fields. The inte-grations over internal photon and graviton lines are performed. The integrals are shown to be conformally invariant and convergent, provided that the new expressions for the propagators are used.