An approach is described which is based on the application to relativistic nuclear physics of similarity laws, the symmetries of solutions, and other methods not based on the Lagrangian method but allowing the construction of models (solutions, laws of Nature) starting from first principles. Our approach permits (1) the determination of the nuclear collision region in which nucleons lose their identity and the energy asymptotes are approached; (2) the prediction and discovery of cumulative processes, demonstrating the observability of multiparticle interactions; (3) the unified description of deep-subthreshold, near-threshold, and cumulative processes; (4) the quantitative description of the final states of nuclear collisions (multiparticle processes) on the basis of the concepts of intermediate asymptotics and the correlation depletion principle in relative four-velocity space; (5) the discovery of local self-similarity of the final states of nuclear collisions; (6) the quantitative description of antimatter production in relativistic nuclear collisions. The main features of the approach are illustrated by the most characteristic experimental data providing justification for our assertions.