Random phase approximation: Difference between revisions

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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>{{cite journal|author=J. Lindhard| journal=Kongelige Danske Videnskabernes Selskab, Matematisk-Fysiske Meddelelser|volume=28|issue=8|year=1954|url=http://gymarkiv.sdu.dk/MFM/kdvs/mfm%2020-29/mfm-28-8.pdf|title=On the Properties of a Gas of Charged Particles}}</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 1950's1950s for overcounting the degrees of freedom and the call for justification led 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 name="Gell-Mann Brueckner pp. 364–368">{{cite journal | last=Gell-Mann | first=Murray | last2=Brueckner | first2=Keith A. | title=Correlation Energy of an Electron Gas at High Density | journal=Physical Review | publisher=American Physical Society (APS) | volume=106 | issue=2 | date=15 April 1957 | issn=0031-899X | doi=10.1103/physrev.106.364 | pages=364–368| url=https://authors.library.caltech.edu/3713/1/GELpr57b.pdf }}</ref>

The consistency in these results became an important justification and motivated a very strong growth in theoretical physics in the late 50's50s and 60's60s.

==Application: RPA ground state of an interacting bosonic system ==