KAPUY LECTURE

Abstract

Several powerful standard procedures for nonrelativistic many-body calculations on atomic and molecular systems exist, such as many-body perturbation theory (MBPT), coupled-cluster approach (CCA), configuration interaction (CI) and multi-configuration Hartree-Fock (MCHF), which all can treat the electron correlation to essentially all orders. Similar techniques can also be applied relativistically within the so-called no-virtual-pair approximation (NVPA). Here, the instantaneous Breit interaction can be included, but effects of retardation and virtual electron-positron pair are neglected, as well as all radiative effects (self energy, vacuum polarization, vertex correction). Effects beyond NVPA are referred to as QED effects (radiative and nonradiative). The standard method for numerical QED calculations is the S-matrix formulation, and other techniques have more recently been developed, the two-times Green\'s function and the covariant evolution operator methods. All these methods have the disadvantage that they can for computational reasons treat only one- and two-photon exchange, which implies that the electron correlation can be included only to lowest order. This is sufficient for heavy, few-electron ions, where relativistic and QED-effects dominate strongly over the electron correlation. For light systems, on the other hand, the situation is the reversed, and two-photon exchange is quite insufficient. Here, it is necessary to include electron correlation to higher orders in order to produce numerical results of interest. By extending the MBPT to include energy-dependent interactions, it is possible to construct a combined many-body-QED procedure, where QED effects can be combined with electron correlation to arbitrary order. Such a procedure, based upon the covariant evolution operator method will be described, and numerical results on heliumlike ions will be given.