New results in conformally invariant quantum field theory

Closed equations for conformal Green functions beyond perturbation theory framework are discussed. Solution to the Ward identities is a very considerable point in their derivation. Therefore, conformal transformations in current, ennergy-momentum tensor and Abelian gauge fields are discussed. A new transformation law for these values is found. In the new formulation of conformal invariance, based on the law, in quantum electrodynamics in the case of weak gravitation there are no difficulties characteristic of the theories in the classical approach. It is shown, that the Maxwell classical equations and conformal gravitation (in the linear approximation) is a consequence of conformal invariance. Explicit equations for 3-point Green functions with the current, corresponding to the new transformation law, are presented. The Ward identities in the new formulation proved to be more informative, than in the old one. All the results are demonstrated using the Thirring model. A theory with spontaneously violated conformal symmetry is considered. The role of quantum corrections for instanton and meron solutions is discussed