Green function for relativistic schroedinger euqation

Using Schroedinger wave function in quantum field theory, the time-dependent Green function and its spectral representation for 2-fermion system are derived, and the Scroedinger equation as well as the normalization condition of his wave function are deduced. The normalization condition shows that this wave function i just the probability amplitude when energy-dependence of potential can be neglected. The Green functions for some other equal-time equations are evaluated, however, the normalization of these equations remains to be solved and the potential is non-Hermitian