  Collective center-of-mass variables are introduced in the Lagrangian
formalism of the relativistic classical mechanics of directly interacting
particles. It is shown that the transition to the Hamiltonian formalism leads
to the Bakamjian-Thomas model. The quantum-mechanical system consisting of two
spinless particles is investigated. Quasi-relativistic corrections to the
discrete energy spectrum are calculated for some Coulomb-like interactions
having field theoretical analogues.
