Some Aspects of Functional Integrals and Many Body Theory

  • David Sherrington
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 34)


Conventionally the quantum many body problem has been formulated in terms of a Hamiltonian language. In second quantization this involves the use of field operators which obey commutation (for bosons) or anticommutation (for fermions) relations for equal times;
$$ \psi \left( {\underline x ,t} \right)\,\,{\psi ^ + }\left( {\underline x ',t} \right) - {\psi ^ + }\left( {\underline x ',t} \right)\,\,\psi \left( {\underline x ,t} \right)\, = \delta \left( {\underline x - \underline x '} \right) $$
$$ \psi \left( {\underline x ,t} \right)\,\,{\psi ^ + }\left( {\underline x ',t} \right) + {\psi ^ + }\left( {\underline {x'} ,t} \right)\,\,\psi \left( {\underline x ,t} \right)\, = \delta \left( {\underline x - \underline x '} \right) $$
Here, and below, we use x to denote symbolically all the relevant coordinates other than time; i.e. space, spin, etc. The 6-function is to be interpreted as Kronecker or Dirac according to whether the corresponding coordinate element is discrete or continuous.


Partition Function Green Function Spin Glass Functional Integral Perturbation Expansion 
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  1. 1.
    J.S. Bell, 1962, ‘Lectures on the Many Body Problem (Naples Spring School)’ Ed. E.R. Caianiello (New York, London: Academic Press), pp 81–9Google Scholar
  2. 2.
    S.F. Edwards and D. Sherrington, 1967, Proc. Phys. Soc. 90, 3–22ADSCrossRefGoogle Scholar
  3. 3.
    D. Sherrington, 1967, Proc. Phys. Soc. 90, 583–4ADSCrossRefGoogle Scholar
  4. 4.
    D. Sherrington, 1971, J. Phys. C4, 401–416ADSGoogle Scholar
  5. 5.
    L.P. Kadanoff and G. Baym, 1962, ‘Quantum Statistical Mechanics’ (New York; Benjamin)MATHGoogle Scholar
  6. 6.
    D. Sherrington, 1966, Ph. D. thesis (University of Manchester) unpublishedGoogle Scholar
  7. 7.
    B. Mühlschlegel, 1977, these lecturesGoogle Scholar
  8. 8.
    S.F. Edwards, 1955, Proc. Roy. Soc. A 232, 371–6ADSCrossRefMATHGoogle Scholar
  9. 9.
    I.M. Gel’fand and A.M. Yaglom, 1960, J. Hath. Phys. 1, 48–69ADSMATHGoogle Scholar
  10. 10.
    R.L. Stratonovich, 1957, Dokl. Akad. Nauk SSSR 115, 1097–1100 (Sov. Phys. Dokl. 2, 416–9)MathSciNetGoogle Scholar
  11. 11.
    J. Hubbard, 1959, Phys. Rev. Lett. 3, 77–8ADSCrossRefGoogle Scholar
  12. 12.
    B. Mühlschlegel, unpublished notes University of Pennsylvania, referenced by Wang et al, 1969, Phys. Rev. Lett. 23, 92–5CrossRefGoogle Scholar
  13. 13.
    See for example S.K. Ha, 1976, ‘Modern Theory of Critical Phenomena’ (New York: Benjamin) or C. Domb and M.S. Green (ed), 1976, Phase Transitions and Critical Phenomena (New York: Academic Press)Google Scholar
  14. 14.
    S.F. Edwards, 1970, in ‘4th Int. Conf. on Amorphous Materials’ (ed. R.W. Douglas and W. Ellis, New York: Wiley)Google Scholar
  15. 15.
    S.F. Edwards and P.W. Anderson, 1975, J. Phys. F5, 965–74ADSCrossRefGoogle Scholar
  16. 16.
    D. Sherrington and K. Mihill, 1974, Proc. Int. Conf. Mag. (Moscow 1973) Vol. 1 (1), 283–87;Google Scholar
  17. 16a.
    D. Sherrington and K. Mihill, 1974, J. de Phys. 35, C4, 199–201.Google Scholar
  18. 17.
    P.W. Anderson, 1958, Phys. Rev. 109, 1492–1505ADSCrossRefGoogle Scholar
  19. 18.
    See for example the review by K. Fisher, Int. Conf. on Magnetism (Amsterdam 1975)Google Scholar
  20. 19.
    D. Sherrington, 1975, AIP Conf. Proc. 29, 224–228ADSCrossRefGoogle Scholar
  21. 20.
    G. Toulouse, 1977, Comm. Phys. 2, 115–119Google Scholar
  22. 21.
    B.W. Southern, 1976, J. Phys. C9, 4011–4020ADSGoogle Scholar
  23. 22.
    B.R. Coles, A. Tari and H.C. Jamieson, 1974, Proc. L.T. XIII, 414Google Scholar
  24. 23.
    D. Sherrington and S. Kirkpatrick, 1975, Phys. Rev. Lett. 35, 1792–96ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1978

Authors and Affiliations

  • David Sherrington
    • 1
  1. 1.Physics DepartmentImperial CollegeLondonUK

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