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The ground-state fluctuation of polarization P is finite in insulators anddivergent 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 Pfluctuation is finite even in metals, and a generalized sum rule applies. Theboundary-condition dependence is a pure correlation effect, not present at theindependent-particle level. In the longitudinal case div P = -rho, and oneequivalently addresses charge fluctuations: the generalized sum rule reducesthen to a well known result of many-body theory.Comment: 4 pages, no figur

Polarization Fluctuations in Insulators and Metals: New and Old Theories Merge