Random phase approximation: Difference between revisions

Revision as of 19:27, 2 July 2014

Revision as of 16:54, 8 July 2014

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The contribution to the [[dielectric function]] from the total electric potential is assumed to ''average out'', so that only the potential at wave vector '''k''' contributes. This is what is meant by the random phase approximation. The resulting dielectric function, also called the ''[[Lindhard theory|Lindhard dielectric function]]'',<ref>J. Lindhard, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. '''28''', 8 (1954)</ref><ref>N. W. Ashcroft and N. D. Mermin, ''Solid State Physics'' (Thomson Learning, Toronto, 1976)</ref> correctly predicts a number of properties of the electron gas, including [[plasmon]]s.<ref>G. D. Mahan, ''Many-Particle Physics'', 2nd ed. (Plenum Press, New York, 1990)</ref>

The RPA was criticized in the late 50's for overcounting the degrees of freedom and the call for justification leadled to intense work among theoretical physicists. In a seminal paper [[Murray Gell-Mann]] and [[Keith Brueckner]] showed that the RPA can be derived from a summation of leading-order chain [[Feynman diagram]]s in a dense electron gas.<ref>M. Gell-Mann, K.A. Brueckner, Phys. Rev. '''106''', 364 (1957)</ref>

The consistency in these results became an important justification and motivated a very strong growth in theoretical physics in the late 50's and 60's.