Constructive field theory

  • Arthur Jaffel
Quantum Field Theory Main Lectures
Part of the Lecture Notes in Physics book series (LNP, volume 116)


Mass Renormalization Dipole Phase Inverse Correlation Length Hyperscaling Relation Free Field Measure 


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  1. 1.
    The original Osterwalder-Schrader theorem is in Commun. Math. Phys. 31, 83(1973), 42, 281 (1975). A theorem similar to this can be found in J. Glimm and A. Jaffe in “New Developments in Quantum Field Theory and Statisticl Mechanics”, edited by P. Mitter and M. Lévy, 1976 Cargèse Lectures. The version here is contained in our forthcoming book. The case p = 2 (e.g. free field) can be handled with a separate assumption.Google Scholar
  2. 2.
    The ϕ3 4 existence theorem combines J. Glimm and A. Jaffe, Fort. d. Physik 21, 327 (1973) with J. Feldman and K. Osterwalder, Ann. Phys. 97 80 (1976) and with J. Magnen and R. Sénéor, Ann. de l'Inst. H. Poincaré 24, 95 (1976). See Commun. Math. Phys. 56, 237 (1977). The strong coupling theory is given in J. Fröhlich, B. Simon and T. Spencer, Commun. Math. Phys. 50, 79 (1976). Other references can be found in these proceedings, e.g. to the work of Gallavotti et al.Google Scholar
  3. 3.
    References to the construction of P(ϕ)2 models can be found in “Statistical Mechanics and Quantum Field Theory” 1970 Les Houches Lectures, C. DeWitt and R. Stora Editors, Gordon and Breach; in “Mathematics of Contemporary Physics,” R. Streater Editor, 1971 London Mathematical Society Symposium, Academic Press; and in “Constructive Quantum Field Theory” edited by G. Velo and A. Wightman, 1973 Erice Summer School, Springer Lecture Notes in Physics V25. The construction of the Yukawa2 model is given in R. Schrader, Ann. Phys. 70, 412 (1972), E. Seiler, Commun. Math. Phys. _42, 163 (1975), J. Magnen and R. Sénéor, Commun. Math. Phys. 51, 297 (1976) and A. Cooper and L. Rosen, Trans. Am. Math. Soc. 234, 1(1977). The recent work of D. Brydges, J. Fröhlich and E. Seiler on the Higgs2 model is in press in Commun. Math. Phys. and in these proceedings. The 1/n expansion of Kupiainen is also in these proceedings, as is the work in progress of Balaban. Multiphase ϕ2 6 models are studied by K. Gawedzki, Commun. Math. Phys. 59, 117 (1978) and S. Sommers, preprint.Google Scholar
  4. 4.
    See 1973 Erice and 1976 Cargèse Lectures.Google Scholar
  5. 5.
    J. Glimm and A. Jaffe, Ann. l'Inst. H. Poincaré 22, 97 (1975) and in the 1979 Cargèse Lectures, Plenum Press, in press.Google Scholar
  6. 6.
    M. A. Moore, D. Jasnow and M. Wortis, Phys. Rev. Lett. 22, 940 (1969); J. Kincaid, G. Baker and W. Fullerton, LA-UR-79-1575; G. Baker and J. Kincaid, LA-UR-79-2655; J. Le Guillou and J. Zinn Justin, Phys. Rev. Lett. 39, 95 (1977).Google Scholar
  7. 7.
    D. Brydges, Commun. Math. Phys. 58, 313 (1978); D. Brydges and P. Federbush, Commun. Math. Phys., in press; and P. Federbush, these proceedings.Google Scholar
  8. 8.
    M. Kosterlitz and D. Thouless, J. Phys. C5, 1124 (1972).Google Scholar
  9. 9.
    See John D. Weeks, “The Roughening Transition” in 1979 Geilo (Norway) School, to appear.Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Arthur Jaffel
    • 1
  1. 1.Harvard UniversityUSA

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