Relativistic simultaneously coupled multiparticle states

Abstract

To carry out calculations dealing with relativistic multiparticle systems requires making a choice of variables that describe the system. Simultaneously coupled states, wherein n single-particle states are coupled together simultaneously rather than in a stepwise fashion, are defined and the resulting variables compared with stepwise variables. Generalized Racah coefficients that connect stepwise coupled states with simultaneously coupled states are derived for three-particle systems and used to calculate properties of resonances in isobar models. Invariants of simultaneously coupled states include orbital and spin angular momentum variables. It is shown how these variables can be coupled together in exactly the same way as is done nonrelativistically.