Method of two-time Green's functions in the Ising model with transverse field

Two-time Green's functions are used to develop a self-consistent approach to the calculation of the spectrum of collective excitations and the free energy in the Ising model with transverse field. Calculations are also made of all correlation functions with allowance for the singularity of their spectral intensity at zero frequency. The accuracy of the approximation is checked by means of kinematic sum rules. It is shown that the use of these sum rules to determine the order parameter leads to unphysical results.