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

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