Gauge dependence of world lines and invariance of theS-matrix in relativistic classical mechanics

The notion of world lines is studied in the constraint Hamiltonian formulation of relativistic point particle dynamics. The particle world lines are shown to depend in general (in the presence of interaction) on the choice of the equal-time hyperplane (the only exception being the elastic scattering of rigid balls). However, the relative motion of a two-particle system and the (classical)S-matrix are independent of this choice.A preliminary version of this paper was circulated as ICTP, Trieste, Internal Report IC/79/59On leave of absence from Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia 1184, Bulgaria