Self-consistent treatment of dynamical correlation functions using a spectral representation technique

A system of equations resulting from an approximation of the equation of motion of Green functions for correlated electron systems is usually solved using Matsubara technique. In this work we propose an alternative method which works entirely along the real frequency axis. Using the example of the attractive Hubbard model studied in the T-matrix approximation both self-consistently and non-self-consistently we demonstrate how powerful such a treatment is especially when dynamic quantities are calculated.