Covariant formulation of relativistic Hamiltonian theory on the light cone

In the covariant formulation of relativistic hamiltonian theory given in [1–3] the momenta of all physical particles belong to the mass shell. In the vertices of diagrams the total 4-momentum of physical particles and the additional spurion line is conserved. The momentum of the spurion is proportional to the constant time-like vector on which the on-shell $S$-matrix does not depend. In the present paper a version of relativistic hamiltonian theory is developed in which the 4-momentum of the spurion lies on the light cone. Essentially new point in this scheme is a specific regularisation, by means of which the singularities present in all theories formulated in the light cone variables are removed in all diagrams. The unitarity and causality conditions are analysed in detail. It is shown that the choice of the regularisation is determined by the causality condition.