RELATIVISTIC CLUSTER DYNAMICS OF NUCLEONS AND MESONS .1. KINEMATICS AND COVARIANCE

A time-ordered relativistic scattering theory for nucleons and mesons based on clusters rather than individual particles is derived. The S-matrix-type approach provides a recursive hierarchy of Lippmann-Schwinger equations, each describing the dynamical evolution of two-cluster configurations at different levels of the many-body problem. The presentation is restricted to a fixed number of particles; particle absorption and creation are treated in part II. The main concern here are the kinematic aspects of the problem. It is shown that the on-shell results of the formalism are covariant, without requiring negative-energy antiparticle contributions. This is achieved by constructing off-shell T matrices as invariants under a set of energy and momentum transformations which reduce to Lorentz transformations for on-shell energies. The present relativistic formulation is formally equivalent to a previously given nonrelativistic N-body approach.