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

TL;DR

This paper introduces a local reduction method for the Dirac equation to analyze quark interactions, enabling approximate solutions and avoiding unphysical states, with applications to the Charmonium spectrum.

Contribution

A novel local reduction technique for the Dirac equation is developed, improving analysis of multi-body quark systems and applied to Charmonium spectrum modeling.

Findings

The reduction method prevents unphysical states in two-body systems.

Approximate solutions for the Dirac equation are obtained.

The approach successfully models the Charmonium spectrum.

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.