Quantum theory of spontaneous scattering of light and coherent states of three-dimensional Lorentz group

The work is devoted to applications of group-theoretic coherent states to describe the nonlinear optical effects. Important in modern quantum information process of parametric down–conversion is studied. It is shown that the use of superpositions of coherent states of $SU (1,1)$ allows to increase the squeezing of generated photon pairs.