We present an exact equation for the exchange-correlation potential of time-dependent density-functional theory. This relation is derived using a many-particle Green's function formalism due to Keldysh. We furthermore show how this equation can be derived from an action principle. The method presented provides a systematic way to derive correlation contributions to the time-dependent exchange-correlation potential.

• Received 27 December 1995

DOI:https://doi.org/10.1103/PhysRevLett.76.3610