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The concept of the potential acting between charged particles is reviewed within the framework of quantum electrodynamics. The one-photon and two-photon exchange potentials V_1 \gamma and V_2 \gamma are discussed, with attention to the following features: the dependence of V_2 \gamma on the choice of V_1 \gamma, the distinction between FGI (Feynman gauge inspired) and CGI (Coulomb gauge inspired) potentials, and the dependence of the large-r behavior on these choices. A summary of available results for two spin-0 particles, for a spin-0 and a spin 1/2 particle and for two spin-1/2 particles is given. The application of such "scattering potentials" to the calculation of energy levels of bound states is discussed., Comment: 10 pages, LaTex (to appear in Advances in Quantum Chemistry)

Helium was first isolated on Earth in 1895, by Sir William Ramsey. One hundred and one years later, it seems like a good time to review our current theoretical understanding of the helium atom. Helium has played an important role in the development of both quantum mechanics and of quantum field theory. The early history of helium is sketched. Various aspects of the modern theory are described in some detail, including (1) the computation of fine structure to order \alpha^2 Ry and \alpha^3 Ry, (2) the decay of metastable states, and (3) Rydberg states and long-range forces. A brief survey is made of some of the recent work on the quantum field theory of He and He-like ions., Comment: 23 pages, Latex, invited talk presented at "Quantum Systems: New Trends and Methods," at Minsk, June 1996; to appear in the proceedings

In relativistic potential models of quarkonia based on a Dirac-type of equation with a local potential there is a sharp distinction between a linear potential V which is vector-like and one which is scalar-like: There are normalizable solutions for a scalar-like V but not for a vector-like V. It is pointed out that if instead one uses an equation of the no-pair type, which is more natural from the viewpoint of field theory, this somewhat bizarre difference disappears., Comment: LaTeX, 4 pages

In quantum field theory the concept of a Lagrangian interaction density, expressed in terms of fields, is primary. Forces between two particles are regarded as arising primarily from the exchange of quanta of the bosonic fields. Thus, in contrast to nonrelativistic quantum mechanics, the concept of a two-body poten tial is secondary. Potentials are not given a priori but must be defined. Part of the purpose of this talk is to review and discuss the issues involved when such definitions are made. In this context I describe a gauge-independent approach to some aspects of the problem of determining the energy levels of bound states, developed in collaboration with the late G. Feinberg, and report some recent results on the long-range potential associated with two-photon exchange between charged particles., Comment: Revised latex file. Send questions to sucher@umdhep.umd.edu

The amplitude T for "free-free" processes, such as bremsstrahlung or photo- absorption by an electron in the continuum in the presence of an external field, is usually written as the matrix element of the radiation operator taken between two continuum states. However, unlike the case when at least one of the states is bound, as in radiative transitions, electron capture, or the photo-effect, this expression contains an unphysical term, proportional to a delta-function and is not really the physical amplitude Tphys. This continues to be true for both the velocity and length form of the dipole approximation to the amplitude T. We first give an a priori definition of Tphys in terms of the scattering parts of the continuum functions, which has an obvious interpretation in terms of time-ordered diagrams. We then show that when the formal amplitude is modified by a long- distance cutoff, the modified form approaches Tphys as the cutoff is removed. The modified form then serves as a basis for the definition of a physical velocity dipole amplitude and this in turn leads to an equivalent length form of the dipole amplitude. This exercise provides a clear theoretical basis for many extant calculations in which cutoff factors are introduces somewhat ad hoc, as needed.

In the calculation of relativistic effects in the structure of many-electron atoms there are two popular choice for the operator V used to represent the electron-electron interaction. One of these, V(I), is associated with the use of the Coulomb gauge propagator for photons; the other, V(II), is associated with the use of the Feynman gauge propagator. In contrast to V(I), the nonperturbative use of V(II) leads to energy levels which are already incorrect in order (alpha exp 4)m. This fact provides a quantitative argument for preferring V(I) to V(II).

Global identities for delta functions, given by Hiller, Sucher and Feinberg (HSF) are applied to the calculation of the hyperfine structure (HFS) of the ground state of Li. It is shown that use of the HSF identity together with configuration interaction type wavefunctions can yield values of the HFS constant f which are comparable in accuracy to that obtained by Larsson with a 100-term Hylleraas-type wavefunction. The implications of this result for HFS calculations for atoms with many electrons are discussed.

The paper examines parity-violating electric-dipole transitions in He in order to gain insight into the reliability of approximate calculations which are carried out for transitions in many-electron atoms. The contributions of the nearest-lying states are computed with a variety of wave functions, including very simple product wave functions, Hartree-Fock functions and Hylleraas-type wave functions with up to 84 parameters. It is found that values of the matrix elements of the parity-violating interaction can differ considerably from the values obtained from the good wave functions, even when these simple wave functions give accurate values for the matrix elements in question

Two identities are derived for the exact scattering wave function by using the method of Hiller, Sucher, and Feinberg. It is shown that the resulting identities can be used to improve the calculation of positron annihilation cross sections whenever an approximate positron-atom scattering wave function is known. In addition, the advantages of the method are illustrated with a static model for e(+)-H scattering and then with a more realistic polarized orbital approximation.

The paper presents an extension of the identities of Hiller, Sucher, and Feinberg for the evaluation of bound-state matrix elements of delta function operators, to scattering states. Attention is given to the technical difficulties encountered in the application of the scattering-state identities and how they can be overcome, including infrared singularities which arise if Coulomb forces are present and the velocity of the incident particle is small. In addition, both the scattering and bound-state identities are generalized to include spin-dependent contact interactions and spin-dependent Hamiltonians. Finally, it is stressed that the identities can be used to improve the accuracy of calculations of interest for diverse physical phenomena, ranging from positron annihilation to hyperfine structure.