Abstract
The Quantum Field Theory (QFT) is considered in which momenta belong to the space of constant nonzero curvature. The conjugated configurational space is quantized space. It is connected with the momentum space by the Fourier expansion in matrix elements of the group of motions of this space. The generators of the translations in the configurational space are differential - difference operators and can be considered as the generators of the q- deformations of the Poincar\'{e} group. The deformed character of the translations leads to radical modification of the singularities of the field - theoretical functions. As a result, the S - matrix elements do not contain the non-integrable expressions.
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