A local reduction of the Dirac equation applied to the study of quark interactions

Abstract

A general procedure of local reduction for the Dirac equation is introduced to study one-and n-body interacting systems. In the one-body case we show that the reduction allows for an approximate solution of the Dirac equation, correlating the upper and the lower components of the wave function. The two-body case is studied in more detail. We show that the method prevents from introducing spurious, unphysical states. The reduction is also applied to another relativistic equation. Finally, the method is used to construct a specific model in order to study the Charmonium spectrum.