Relativistic Lagrangian Field Theory for Composite Systems

Abstract

It is shown that infinite-component field theories provide a useful alternative to the Bethe-Salpeter equation as a fully relativistic treatment of composite systems. Scattering amplitudes obtained by models of this type satisfy both Mandelstam analyticity and conspiracy requirements. Current algebras are saturated with a combination of discrete and continuous spectra. Most of the paper is devoted to a special example, for which it is found that the mass spectrum has a discrete part (bound states) and a continuous part (scattering states); that the metric in physical Hilbert space is positive definite; and that vertex functions and scattering amplitudes are analytic functions of $s$ and $t$, with singularities at the same locations as in local field theory. The role of "spacelike solutions" is studied in detail, with some surprising results.