Time-dependent exchange-correlation potential in lieu of self-energy

TL;DR

The paper introduces a time-dependent exchange-correlation potential that governs the Green function's equation of motion, offering a new approach to many-electron system analysis through the exchange-correlation hole.

Contribution

It proposes a formalism where the Green function is governed by a time-dependent exchange-correlation potential derived from the exchange-correlation hole, generalizing static sum rules.

Findings

The exchange-correlation hole satisfies a sum rule extending the static case.

The formalism suggests an alternative method for calculating Green functions.

Potential for approximations using local-density or similar methods.

Abstract

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.