Higher Random-Phase Approximations and the Theory of the Electron Gas

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Using the example of the degenerate electron gas, it is shown how the operator equations of motion for a manyparticle system may be exploited to generate systematically a sequence of nonperturbative approximations of which some version of the random phase approximation is the first. Some questions left unsettled by previous attempts in this direction are resolved by close attention to the structure of the spectrum of the system. The solution of the equations is carried only so far as to make contact with previously substantiated results. Finally, a rigorous proof is given that the plasmon frequency approaches the classical plasmon frequency in the longwavelength limit. (auth)