Relativistic equations and quark confinement problem

The Dirac equation in an external field with infinitely rising central potential, which is a fourth component of the Lorentz-vector, has only continuous spectrum owing to a leakage into infinite barrier (the Klein paradox). The same situation happens in the Breit equation. It is known that the inclusion of the Lorentz-scalar potential changes this undesirable property. From theoretical point of view vector interaction is preferable, because the color gluons, by exchange of which the strong force between quarks is generated, are vector particles. On the other hand, all relativistic equations for both potentials are reduced to the same Schrodinger equation, in the framework of which quarkonium (bound states of quark and antiquark) spectrum is described theoretically rather well. For a long time it was unclear which relativistic equation will be more suitable for quarkonium problems. Below we consider the most general quasipotential equation for spin-1/2 quarks, which was derived by one of the authors (A.K.). This equation involves full information of the quantum field theory and is 3-dimensional. In particular cases it follows all the known three dimensional equations. The quasipotential contains projective operators in case of instantaneous kernels and reduces to the Salpeter equation. These projective operators in a reasonable approximation induce scalar potential from the vector one. Therefore, the Klein paradox is avoided. As a result, bound state solutions appear. At last, the obtained earlier radial equation is exhibited and the confinement phenomenon is demonstrated. (author)