Conformal quantum space $SU(2,2)\simeq O(2,4)$ with Poincare group of   motion
  It is shown that algebra of quantum space of the title of the present paper may be realized on usual unphysical Minkowskii one. Equations of field theory and there solutions are discussed. Solution equations of particle motion are obtained in implicit form from the classical ones. 
A. N. Leznov