  The ground-state fluctuation of polarization P is finite in insulators and
divergent in metals, owing to the SWM sum rule [I. Souza, T. Wilkens, and R. M.
Martin, Phys. Rev. B 62, 1666 (2000)]. This is a virtue of periodic (i.e.
transverse) BCs. I show that within any other boundary conditions the P
fluctuation is finite even in metals, and a generalized sum rule applies. The
boundary-condition dependence is a pure correlation effect, not present at the
independent-particle level. In the longitudinal case div P = -rho, and one
equivalently addresses charge fluctuations: the generalized sum rule reduces
then to a well known result of many-body theory.
