On the Dirac equation for a quark

TL;DR

This paper proposes a modified Dirac equation for quarks within QCD, ensuring the correspondence principle and deriving an interquark potential that matches the Coulomb law and Cornell potential.

Contribution

It introduces a new Dirac equation for quarks consistent with QCD and the correspondence principle, linking it to known interquark potentials.

Findings

Interquark potential follows Coulomb law

Potential coincides with Cornell potential

Modified Dirac equation is consistent with QCD

Abstract

It is argued from geometrical, group-theoretical and physical points of view that in the framework of QCD it is not only necessary but also possible to modify the Dirac equation so that correspondence principle holds valid. The Dirac wave equation for a quark is proposed and some consequences are considered. In particular, it is shown that interquark potential expresses the Coulomb law for the quarks and, in fact, coincides with the known Cornell potential.