In the framework of Bogolubov'a axiomatic approach problems connected with the extension of the scattering matrix off the mass shell are considered. A specific point for the standard extension procedure is the assumption that the four dimensional Space of virtual momenta in which the extended objects (fields, currents, S-matrix coefficient functions, etc) are defined is flat Min¬kowski apace. However, such a choice of the geometry of the virtual momentum space does not follow from the basic axioms of the theory and in feet is an independent postulate. In our opinion the pseude-euclidean momentum space is not adequate for the description of the phenomena at high energies (short distances). We suppose that the use of Minkowski p-space is actually responsible, for the known difficulties of the local quantum field theory connected with the problem of multiplying of distributions with coinciding singula¬rities on the light cone. As an alternative we propose to use in the extension of the S-matrix a 4-momenturn space of constant cur¬vature (De-Sitter space) with curvature radius 1/ξ, where ξ is a fundamental length. The interaction laws of the elementary particles at large momenta are completely different in the new scheme.nThe off-mass-shell S-matrix extension in the spirit of De-Sitter p-apace geometry is consistent with the requirements of Poincare invariance, unitarity, spectrality, completeness of the system of asymptotic states. With the help of a Fourier transfor¬mation in De-Sitter momentum space a new configuration ζ-space is introduced, whose geometry for small distances ≤& is essen¬tially different from the paeudoeuclidean one. The causality con¬dition which is direct generalization of Bogolubov's causality condition, going to it in the limit ξ→0, is formulated in terms of this ζ -space. It is demonstrated that in the developed theory the problem of distribution products loses its acuteness. In particular the commutation functions and propagators in the new scheme are usual (not generalized) functions and there is no arbitrariness in any their powers and products.
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