Relativistic cluster dynamics of nucleons and mesons. II. Formalism and examples.

A time-ordered manifestly covariant relativistic scattering theory for arbitrarily large systems of nucleons and mesons is derived. The [ital S]-matrix-type approach is based on clusters rather than individual particles; it provides a recursive hierarchy of Lippmann-Schwinger equations, each describing the dynamical evolution of two-cluster configurations at different levels of the relativistic many-body problem. The present work extends the results of part I to include particle absorption and creation. The resulting effective two-body equations describe all possible absorption and production processes up to the maximum number of initially considered particles; they employ fully dressed cluster propagators and vertices, including all crossed meson contributions. Nonlinear couplings introduce effective contributions from infinitely many mesons. Examples of pion-nucleon, pion-deuteron, and nucleon-nucleon scatterings are discussed. An algorithm for the self-consistent implementation of crossing symmetry and for the determination of the off-shell [pi][ital N] form factor is given. Implications for crossing mechanisms employed in [ital NN] potentials and for novel types of three-body forces in three-nucleon calculations are pointed out.