Remark to the field theory with quantiгed space-time

We examine the theory of quantized space-time developed by V. G. Kadyshevskii and co-workers. In this theory momentum space is a surface of constant curvature: $(π^0)^2 — (π^1)^2 - (π^2)^2 — (π^3)^2 + (π^4)^2 = 1$. Each value of the physical four-momentum $p^μ= π^μ$(μ = 0, 1, 2, 3) corresponds to two points in momentum space π and $π^*$, which differ by the ii sign of $π^4$. Using the conditions of translational invariance and the microcausality of the S matrix, we show that the retarded functions for n ≥ 2 satisfy the relation $R_{n}(π_{0}{1},..., π_{n})= -R_{n}(π_{0}^{*},π_{1},...,π_{n})$ which connects the values of the matrix elements in the region $π^{4}>0$ with the values of the matrix elements in the region $π^{4}<0$.