The divergence representation of the exact stress force: Implications for density-functional theory

We prove that the local stress force in a quantum many-body system is representable in a form of a divergence of a symmetric second rank tensor, provided that the interparticle interaction satisfies the Newton's third law. The above divergence theorem allows to formulate the exact local constraints on the exchange-correlation potentials both in the static and in time-dependent density functional theory. We show that the well known zero-force and zero-torque sum rules represent a particular consequence of our new local condition.