The Uses of Conformal Symmetry in QCD

The Lagrangian of Quantum Chromodynamics is invariant under conformal transformations. Although this symmetry is broken by quantum corrections, it has important consequences for strong interactions at short distances and provides one with powerful tools in practical calculations. In this review we give a short exposition of the relevant ideas, techniques and applications of conformal symmetry to various problems of interest.Comment: 110 pages, invited review for "Prog. Part. Nucl. Phys

Two-time Green function method in quantum electrodynamics of high-Z few-electron atoms

The two-time Green function method in quantum electrodynamics of high-Z few-electron atoms is described in detail. This method provides a simple procedure for deriving formulas for the energy shift of a single level and for the energies and wave functions of degenerate and quasi-degenerate states. It also allows one to derive formulas for the transition and scattering amplitudes. Application of the method to resonance scattering processes yields a systematic theory for the spectral line shape. The practical ability of the method is demonstrated by deriving formulas for the QED and interelectronic-interaction corrections to energy levels and transition and scattering amplitudes in one-, two-, and three-electron atoms. Numerical calculations of the Lamb shift, the hyperfine splitting, the bound-electron g factor, and the radiative recombination cross section in heavy ions are also reviewed.Comment: 92 pages, 39 figures, 7 table