Three-Dimensional Covariant Integral Equations for Low-Energy Systems

Publisher Website
Google Scholar
Abstract
Integral equations suitable for the dynamical treatment of strongly interacting particles are derived. The equations can be described as Bethe-Salpeter equations with one particle restricted to the mass shell, resulting in a three-dimensional covariant equation which can be easily interpreted physically. To restore the dynamical terms omitted in the process of restricting one particle to the mass shell, additional kernels are added to the irreducible kernels from the original Bethe-Salpeter equation. The addition of these extra terms leads to a resulting simplification in the kernels themselves, since the new kernels have the same structure as the original ones, with some partial cancellations. Estimates as to the convergence of the procedure and the sizes of the various potentials are given. The special case of the hydrogen atom is discussed briefly, and comments are made on the application of these equations to the nuclear-force problem. Connections between scattering equations and bound-state equations are discussed, and the relativistic normalization condition for bound-state wave functions is derived.