Interacting Particles, II: Fock Space Formulation

  • Walter T. GrandyJr.
Part of the Fundamental Theories of Physics book series (FTPH, volume 19)


The calculational techniques developed around the notion of clustering in the preceding chapter are obviously powerful, particularly as applied to the virial series. But, just as with methods of statistical analysis in general, no calculational scheme is likely to be universally optimal. Cluster-related techniques appear most efficient at moderate to high temperatures, although they certainly can be extended to the study of low-temperature phenomena, as already demonstrated.


Annihilation Operator Symmetry Number Grand Partition Function Calculational Scheme Ring Diagram 
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  1. Adhikari, S.K., and R.D. Amado: 1971, ‘Low-Temperature Behavior of the Quantum Cluster Coefficients’,Phys. Rev. Letters 27, 485.ADSCrossRefGoogle Scholar
  2. Alers, G.A., and J.R. Neighbours: 1959, ‘Comparison of the Debye ө Determined from ElasticConstants and Calorimetry’, Rev. Mod. Phys. 31, 675.ADSCrossRefGoogle Scholar
  3. Bogoliubov, N.N.: 1947, ‘On the Theory of Superfluidity’, J. Phys. U.S.S.R.) 11, 23.Google Scholar
  4. Born, M., and Th. von Karman: 1912, ‘Uber Schwingungen in Raumgittern’, Phys. Z. 13, 297Google Scholar
  5. Brueckner, K.A.: 1955, ‘Many-Body Problem for Strongly Interacting Particles.II. Linked ClusterExpansion’, Phys. Rev. 100, 36.ADSzbMATHCrossRefGoogle Scholar
  6. Carr, W.J., Jr., R.A. Coldwell-Horsfall, and A.E. Fein: 1961, ‘Anharmonic Contribution to the Energy of a Dilute Electron Gas— Interpolation for the Correlation Energy’, Phys. Rev. 124, 747.ADSzbMATHCrossRefGoogle Scholar
  7. Carr, W. J., Jr., and A.A. Maradudin: 1964, ‘Ground-State Energy of a High-Density Electron Gas’, Phys. Rev. 133, A371.ADSCrossRefGoogle Scholar
  8. Chandrasekhar, S.: 1931, ‘The Highly Collapsed Configurations of a Stellar Mass’, Mon. Not. Roy.Astron. Soc. 91, 456.ADSzbMATHGoogle Scholar
  9. Debye, P.: 1912, ‘Zur Theorie der spezifischen Wärme’, Ann. d. Phys. 39, 789.ADSCrossRefGoogle Scholar
  10. Debye, P., and E. Hückel: 1923, ‘Zur Theorie der Elektrolyte’, Phys. Z. 24, 185, 305.Google Scholar
  11. DuBois, D.F.: 1959, ‘Electron Int er act ions. Part I. Field Theory of a Degenerate Electron Gas’,Ann. Phys. (N.Y.) 7, 174.ADSzbMATHCrossRefGoogle Scholar
  12. Dyson, F.J., and A. Lenard: 1967, ‘Stability of Matter.I’, J. Math. Phys. 8, 423.MathSciNetADSzbMATHCrossRefGoogle Scholar
  13. Efimov, V.N., and M.Ya. Amus’ya: 1964, ‘Ground State of a Rarefied Fermi Gas of Rigid Spheres’, J. Exptl Theor. Phys. (U.S.S.R.) 47, 581 [English translation, 1965: Sov. Phys. JETP 20, 388.].Google Scholar
  14. Einstein, A.: 1907, ‘Die Plancksche Theorie der Strahlung und die Theorie der spezifischen Wärme’, Ann.d. Phys. 22, 180.ADSGoogle Scholar
  15. Fetter, A.L., and J.D. Walecka: 1971, Quantum Theory of Many-Particle Systems, McGraw-Hill, New York.Google Scholar
  16. Fine, P.C.: 1939, ‘The Normal Modes of Vibration of a Body-Centered Cubic Lattice’, Phys. Rev. 56, 355.ADSzbMATHCrossRefGoogle Scholar
  17. Fisher, M.E., and D. Ruelle: 1966, ‘The Stability of Many-Particle Systems’, J. Math. Phys. 7, 260.MathSciNetADSCrossRefGoogle Scholar
  18. Fock, V.: 1930, ‘Näherungsmethode zur Lösung des quantenmechanischen Mehrkörperproblems’, Z. Phys. 61, 126.ADSCrossRefGoogle Scholar
  19. Fock, V.: 1932, ‘Konfigurationsraum und zweite Quantelung’, Z. Phys. 75, 622.ADSzbMATHCrossRefGoogle Scholar
  20. Gell-Mann, M.: 1957, ‘Specific Heat of a Degenerate Electron Gas at High Density’, Phys. Rev. 106, 369.MathSciNetADSzbMATHCrossRefGoogle Scholar
  21. Gell-Mann, M., and K.A. Brueckner: 1957, ‘Correlation Energy of an Electron Gas at High Density’, Phys. Rev. 106, 364.MathSciNetADSzbMATHCrossRefGoogle Scholar
  22. Ginibre, J.: 1968, ‘On the Asymptotic Exactness of the Bogoliubov Approximation for Many BosonSystems’, Commun. Math. Phys. 8, 26.MathSciNetADSzbMATHCrossRefGoogle Scholar
  23. Ginibre, J., and G. Velo: 1968, ‘On the Bogoliubov Approximation for Many-Boson Systems’, Phys. Letters 26A, 517.ADSGoogle Scholar
  24. Goldstone, J.: 1957, ‘Derivation of the Brueckner Many-Body Theory’, Proc. Roy. Soc. (London) A239, 267.MathSciNetADSGoogle Scholar
  25. Grandy, W.T., Jr.: 1970, ‘Intrinsic Quantum Behavior of the Fully Ionized Gas’, Nuovo Cimento 65B, 73.ADSGoogle Scholar
  26. Grandy, W.T., Jr., and F. Mohling: 1965, ‘Quantum Statistics of Fully Ionized Gases’, Ann. Phys. (N.Y.) 34, 424.ADSCrossRefGoogle Scholar
  27. Hartree, D.R.: 1928, ‘The Wave Mechanics of an Atom with a Non-Coulomb Central Field.Part I.Theory and Methods’, Proc. Camb. Phil Soc. 24, 89.ADSCrossRefGoogle Scholar
  28. Henshaw, D.G., and A.D.B. Woods: 1961, ‘Modes of Atomic Motions in Liquid Helium by InelasticScattering of Neutrons’, Phys. Rev. 121, 1266.ADSCrossRefGoogle Scholar
  29. Hertel, P., and W. Thirring: 1971, ‘Free Energy of Gravitating Fermions’, Commun. Math. Phys. 24, 22.MathSciNetADSzbMATHCrossRefGoogle Scholar
  30. Hwang, I.-K., and W.T. Grandy, Jr.: 1969, ‘Theory of Photons in a Fully Ionized Gas.I. PhotonMomentum Distribution’, Phys. Rev. 177, 359.ADSCrossRefGoogle Scholar
  31. Jordan, P., and E.P. Wigner: 1928, ‘Über das Paulische Äquivalenzverbot’, Z. Phys. 47, 631ADSCrossRefGoogle Scholar
  32. Kawasaki, K., and I. Oppenheim: 1965, ‘Logarithmic Term in the Density Expansion of TransportCoefficients’, Phys. Rev. 139, A1763.MathSciNetADSCrossRefGoogle Scholar
  33. Keller, W.E.: 1969, Helium-3 and Helium-4, Plenum Press, New York.Google Scholar
  34. Landau, L.D.: 1941, ‘The Theory of Superfluidity of Helium II’, J. Phys. (U.S.S.R.) 5, 71.Google Scholar
  35. Landau, L.D.: 1944, ‘On the Hydrodynamics of He II’, J.Phys. (U.S.S.R.) 8, 1.Google Scholar
  36. Landau, L.D.: 1947, ‘On the Theory of Superfluidity of Helium II’, J.Phys. (U.S.S.R.) 11, 91.[Landau's Russian articles are translated into English in: D. ter Haar (ed.), Collected Papers of L.D. Landau, Gordon and Breach, New York, 1965.]Google Scholar
  37. Leighton, R.B.: 1948, ‘The Vibrational Spectrum and Specific Heat of a Face-Centered CubicCrystal’, Rev. Mod. Phys. 20, 165.ADSCrossRefGoogle Scholar
  38. Lenard, A., and F.J. Dyson: 1968, ‘Stability of Matter,II’, J. Math. Phys. 9, 698.MathSciNetADSzbMATHCrossRefGoogle Scholar
  39. Levy-Leblond, J.-M.: 1969, ‘Nonsaturation of Gravitational Forces’, J. Math. Phys. 10, 806.ADSCrossRefGoogle Scholar
  40. Lynden-Bell, D., and R. Wood: 1968, ‘The Gravo-Thermal Catastrophe in Isothermal Spheres and the Onset of Red-Giant Structure for Stellar Systems’, Mon. Not. Roy. Astron. Soc. 138, 495.ADSGoogle Scholar
  41. Macke, W.: 1950, ‘Uber die Wechselwirkungen im Fermi-Gas’, Z. Naturforsch. 5a, 192.ADSGoogle Scholar
  42. Mohling, F., and W.T. Grandy, Jr.: 1965, ‘Quantum Statistics of Multicomponent Systems’, J. Math. Phys. 6, 348.MathSciNetADSCrossRefGoogle Scholar
  43. Rice, S.A., and P. Gray: 1965, The Statistical Mechanics of Simple Liquids, Interscience (Wiley), New York, p.22.Google Scholar
  44. Salzberg, A.M.: 1965, ‘Exact Statistical Thermodynamics of Gravitational Interactions in One andTwo Dimensions’, J. Math. Phys. 6, 158.MathSciNetADSzbMATHCrossRefGoogle Scholar
  45. Schick, M., and T.M. Wu: 1969, ‘Charged Bose Gas’, Phys. Rev. 177, 313.ADSCrossRefGoogle Scholar
  46. Spruch, L.: 1986, ‘Retarded, or Casimir, Long-Range Potentials’, Physics Today, November, p.37.Google Scholar
  47. Thirring, W.: 1970, ‘Systems with Negative Specific Heat’, Z. Phys. 235, 339.ADSCrossRefGoogle Scholar
  48. Thouless, D.J.: 1972, The Quantum Mechanics of Many-Body Systems,2nd ed., Academic Press, New York.Google Scholar
  49. Wick, G.C.: 1950, ‘The Evaluation of the Collision Matrix’, Phys. Rev. 80, 268.MathSciNetADSzbMATHCrossRefGoogle Scholar
  50. Wigner, E.: 1934, ‘On the Interaction of Electrons in Metals’, Phys. Rev. 46, 1002.ADSzbMATHCrossRefGoogle Scholar
  51. Wigner, E.P.: 1938, ‘Effects of the Electron Interaction on the Energy Levels of Electrons in Metals’,Trans. Faraday Soc. 34, 678.CrossRefGoogle Scholar
  52. Wigner, E.P.: 1960, ‘The Unreasonable Effectiveness of Mathematics in the Natural Sciences’,Commun. Pure Appl. Math. 13, 1zbMATHCrossRefGoogle Scholar
  53. Wu, T.T.: 1959, ‘Ground State of a Bose System of Hard Spheres’, Phys. Rev. 115, 1390.MathSciNetADSzbMATHCrossRefGoogle Scholar
  54. Wilks, J.: 1967, The Properties of Liquid and Solid Helium, Clarendon Press, Oxford.Google Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1987

Authors and Affiliations

  • Walter T. GrandyJr.
    • 1
  1. 1.Department of Physics and AstronomyUniversity of WyomingUSA

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