  It is shown that the equation of motion of the one-particle Green function of
an interacting many-electron system is governed by a multiplicative
time-dependent exchange-correlation potential, which is the Coulomb potential
of a time-dependent exchange-correlation hole. This exchange-correlation hole
fulfills a sum rule, a generalization of the well-known sum rule of the static
exchange-correlation hole. It is envisaged that the proposed formalism may
provide an alternative route for calculating the Green function by finding a
suitable approximation for the exchange-correlation hole or potential based on,
e.g., a local-density approximation.
