Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-04-04
Physics
High Energy Physics
High Energy Physics - Theory
LATEX, 33 pages
Scientific paper
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.
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