Abstract:
A non-equilibrium Ward Identity (NE WI) connecting the scalar transport vertex correction with one-particle self-energy is derived using the global U(1) symmetry of the Fermion non-equilibrium Green's functions (NGF). The non-perturbative derivation does not depend on the details of the many-body system. A renormalized multiplicative composition rule for NGF, reflecting time coherence, is obtained and related to NE WI. Applications involve: (i) testing the consistency of approximations shown on the example of self-consistent Born approximation for disorder scattering, (ii) in the general quantum transport theory, the formalism permits to assess routes to generalized master equations, in particular those based on the Generalized Kadanoff-Baym Ansatz.