Abstract:
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.
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