Frequency-dependent susceptibility of a free electron gas in D dimensions

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Abstract
The real and imaginary parts of the dynamic susceptibility of a free electron gas at T=0 are obtained as a function of wave vector k, frequency ω, and space dimensionality D. The real part of the dynamic susceptibility is shown to be simply related to the static susceptibility. For odd-numbered dimensions there exists a general dimensional relationship for the dynamic susceptibility, originating from a similar relationship for the static susceptibility. For even-numbered dimensions there is no such general relationship, but instead a restricted one.