Abstract
We compare two dynamical mean-field theories for the calculation of the dielectric response function \ensuremath{\epsilon}(k\ensuremath{\omega}) of a strongly coupled Coulomb liquid. The two approximations share the feature that they express the correlational part of the linear response function in terms of the quadratic response function. We point out that even though the two approaches, the velocity-average approximation of Golden and Kalman [Phys. Rev. A 19, 2112 (1979)] and the universal mean-field approximation of Tao and Kalman [Phys. Rev. A 43, 973 (1990)], start from entirely different premises, they lead to the same result as to how the linear and quadratic response functions are related. On the other hand, they ultimately differ from each other in the way they break up the quadratic response function in order to achieve self-consistency.
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