Update on a QED Book Project*

For more than 60 years, the book of Bethe and Salpeter has been a cornerstone

in the description of few-body atomic systems. An update may be indicated.

Starting from the basic nonrelativistic and relativistic formulas for the

hydrogen bound and continuum states, we proceed to discuss Green functions

(including Schwinger's momentum representation of the Schrödinger-Coulomb

Green function and its derivation) in detail. The calculation of Bethe logarithms

is discussed. Interaction potentials are derived by matching scattering amplitudes

and effective Hamiltonians. Higher-order effects are an integral part of the

treatment, and so is the

calculation of the helium spectrum, including relativistic and radiative corrections.

Relativistic recoil corrections are discussed in detail, using various

methods, i.e., the Bethe-Salpeter equation and nonrelativistic quantum

electrodynamics (NRQED).

Further topics include the renormalization group, field-theory methods, and

vacuum-mediated corrections to photon propagators. The book serves both

as a textbook as well as a monograph and is currently in the very final proofreading

stages. The book contains a number of hitherto unpublished results, e.g.,

concerning the scaling properties of wave functions and connections to 

virial theorems, and general higher-order effects.