Covariant three-dimensional formulation of the composite quark model of mesons

The quasipotential approach is used to develop a three-dimensional covariant formalism for the description of composite systems of two relativistic particles. The mathematical formalism employs Lobachevskii geometry and an expansion with respect to the matrix elements of unitary (infinite-dimensional) representations of the Lorentz group. The use of harmonic analysis on the Lorentz group instead of an ordinary Fourier transformation makes it possible to go over from an integral equation to a finite-difference equation, this being a covariant three-dimensional generalization of the Schrödinger equation; it permits the finding of exact solutions.