ON THE DYSON EQUATION AND THE WARD-TAKAHASHI IDENTITIES OF THE CLOSED TIME PATH GREEN'S FUNCTIONS

The Dyson equation satisfied by the closed time path Green's function of the or-der parameters is considered.The transport equation for the number density of thequasi-particles is written down in a general but simple form.Using the path integ-ral formulation for the generating functional of these Green's functions,the Ward-Takahashi identities are deduced.