## Correlation Energy of an Electron Gas at High Density (Gell-Mann and Brueckner, pp. 364-369) WITH Specific Heat of a Degenerate Electron Gas at High Density (Gell-Mann, pp. 369-372) in Physical Review 106, Number 2, April 15, 1957

Lancaster: American Institute of Physics, 1957. 1st Edition. FIRST EDITION IN ORIGINAL WRAPS OF 2 IMPORTANT PAPERS BY MURRAY GELL-MANN, THE 1st A “FAMOUS PAPER” IN WHICH GELL-MANN & BRUECKNER SHOW THAT RANDOM PHASE APPROXIMATION (RPA) CAN BE DERIVED BY SUMMING A SERIES OF FEYNMAN DIAGRAMS IN A DENSE ELECTRON GAS (WP; Ren, RPA, 2-3). Presenting a detailed calculation for the ground state energy of the interacting electron gas in the high density limit, this work (and another by Goldstone) represents “the earliest example…of the application of Feynman-type diagrammatic methods in condensed-matter theory” (ibid). “The consistency in [Gell-Mann & Brueckner’s] results became an important justification and motivated a very strong growth in theoretical physics in the late 50's and 60's” (IPFS, RPA).

The second paper, authored by Gell-Mann alone, generalizes the methods he & Brueckner developed “so that not only the ground state but also the low excited states of an electron gas can be discussed”; he also applies the new quantum field theoretical methods and calculates the specific heat of the high-density homogeneous electron gas” (Gell-Mann, 1957).

While a consultant at the RAND in 1956, Gell-Mann, “was involved in a project concerned with correcting the Fermi-Thomas model for electrons in an atom. One correction, the correlation energy of the electrons, could be studied in a related but simplified situation – that of an electron gas in a uniform positive background” (Gell-Mann, Phil Mag, 74, p 432, 1996).

Others had studied the correlation energy -- a measure of how much the movement of one electron is influenced by the presence of all other electrons. However their work had been criticized “for overcounting the degrees of freedom” and other divergences (IPFS). And, though “good work had…been done by David Pines on the correlation energy of an electron gas at high densities, in the straightforward perturbation calculation one of the terms diverged and on that term more work was needed. Wigner, too, “calculated the energy of such a gas in the very high density and very low density limits [but then] guessed an approximation yielding a form to interpolate at the interesting intermediate densities of electrons…RAND physicists thought that it would be useful to calculate corrections to the high-density limit in a systematic way, using an expansion, in order to get a handle on how the formula actually behaved as it neared the intermediate density region from the high density end” (GM, Phil Mag).

[Gell-Mann] studied the leading divergences to each order of perturbation theory and worked on summing them [to] obtain a finite answer containing a logarithm of density” (ibid). Working together, he and fellow physicist Keith Brueckner employed a diagrammatic approach for treating electron interactions in a degenerate electron gas and were able to eliminate the divergences of the previous approaches and complete Pines’ earlier calculation of the high-density correlation energy.

Gell-Mann & Brueckner “published their calculation of the ground-state energy of the interacting electron gas in the high-density limit” in this paper (Joas, Quantum History). By building on “knowledge of and previous training in nuclear many-body theory and quantum electrodynamics”, it is arguagbly the first systematic application of Feynman diagrammatic methods to the solid state (ibid). “A seminal result, it is often considered to be the first major accomplishment of modern quantum many-particle theory and has been an inspiration for the entire field” (WP). “Little did [Gell-Mann & Brueckner] foresee the imminent burst of activity in the field of solid state physics, entailing the successful application of field-theoretic many-body techniques to a plethora of previously unsolved problems” (Joas). Item #1160

CONDITION & DETAILS: 4to. 10.5 x 7.75 inches. Bound in original wraps re-backed. Very faint stamp on the front and rear wrap as well as the first page; difficult to see (see photos). Bright and clean inside and out.

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Price:
$300.00
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