Retarded/Advanced Correlation Functions and Soft Photon Production in the Hard Loop Approximation

We apply the retarded/advanced formalism of real time field theory to the QED or QED like case. We obtain a general expression for the imaginary part of the two-point correlation function in terms of discontinuities. The hard loop expansion is derived. The formalism is used to extract the divergent part of the soft fermion loop contribution to the real soft photon production.