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151) Notice that the residue is determined by the exact density and by the bare mass. This is a consequence of Galilean Invariance.

LINEAR RESPONSE THEORY 30 which is known as the f -sum rule. If the system is isotropic, these relations can be used to yield a simpler form for the conductivity tensor. 141) for all p. 144) ⊥ These relations tell us that the real part of σ is determined by the imaginary part of D ret . Thus, the resistive part of σ (which is responsible for dissipation in the system) is determined by the imaginary part of a response function. This is generally the case. 9. , a plasmon R branch. 145) reg R where A(p, ω) is the residue, and D00 is regular (analytic) near the plasma reg branch.

149) Hence, A=− (typically A(ω) = A∗ (−ω)). 150) CHAPTER 4. 151) Notice that the residue is determined by the exact density and by the bare mass. This is a consequence of Galilean Invariance.