Coherent states on lie groups and evolution operator of a system of interacting bosons and fermions

Matrix elements of the evolution operator of boson-fermion system between coherent states are calculated by means of the method of coherent states on the Lie groups. It is shown that the dynamics of a quantized system of interacting bosons and fermions with finite number of the degrees of freedom and three-particle interaction Hamiltonian can be described by means of a certain trajectory in the direct product of the rotation group and the group of border matrices. Differential equation determining this trajectory is derived.