Classical Relativistic Mechanics of Interacting Point Particles

The possibility of formulating a classical relativistically invariant mechanics of an arbitrary number of interacting point particles is demonstrated. This theory is similar to Newtonian mechanics inasmuch as the interaction between any pair of particles contains an arbitrary function of their distance. The conservation laws for energy and linear and angular momenta are established in the sense that the sum of these quantities for the particles entering a collision is equal to the corresponding sum for the collision products. The possibility of such a mechanics contrasts with the impossibility, demonstrated recently, of establishing a relativistic mechanics within the framework of the canonical representations of the Lorentz group.