  Conformal group of transformations in the momentum space, consisting of
translations $p'_{\mu}=p_{\mu}+h_{\mu}$, rotations
$p'_{\mu}=\Lambda^{\nu}_{\mu}p_{\nu}$, dilatation $p'_{\mu}=\lambda p_{\mu}$
and inversion $p'_{\mu}= -M^2p_{\mu}/p^2$ of the four-momentum $p_{\mu}$, is
used for the five dimensional generalization of the equations of motion for the
interacting massive particles. It is shown, that the ${\cal S}$-matrix of the
charged and the neutral particles scattering is invariant under translations in
a four-dimensional momentum space $p'_{\mu}=p_{\mu}+h_{\mu}$. In the suggested
system of equations of motion, the one-dimensional equations over the fifth
coordinate $x_5$ are separated and these one dimensional equations have the
form of the evaluation equations with $x_5=\sqrt{x_o^2-{\bf x}^2}$. The
important property of the derived five dimensional equations of motion is the
explicit separation of the parts of these equations according to the inversion
$p'_{\mu}=-M^2 p_{\mu}/p^{2}$, where $M$ is a scale constant.
