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

Three-dimensional covariant formalism for describing composite systems of two relativistic particles is developed in the framework of the quasipotential approach. Mathematical apparatus of the formalism includes the Lobachevsky geometry and the expansion in matrix elements of unitary (infinite-dimensional) representations of the Lorentz group. Using the harmonic analysis on the Lorentz group instead of the usual Fourier transformation makes it possible to pass from the integral equation to the equation in finite differences which represents the three-dimensional covariant generalization of the Schroedinger equation and admits obtaining exact solutions