Communications in Mathematical Physics

, Volume 56, Issue 3, pp 237–276 | Cite as

Phase space cell expansion and borel summability for the Euclidean φ34 theory

  • J. Magnen
  • R. Sénéor


The stability of the free energy is proved for complex values of the coupling constant by the way of a convergent expansion. As a consequence, one obtains the Borel summability of the perturbation series.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Glimm, J., Jaffe, A.: Positivity of the φ34 hamiltonian. Fortschr. Physik21, 327–376 (1973)Google Scholar
  2. 2.
    Glimm, J., Jaffe, A., Spencer, T.: In: Constructive quantum field theory. Lecture notes in physics, Vol. 25. Berlin-Heidelberg-New York: Springer 1973Google Scholar
  3. 3.
    Simon, B.: TheP(φ)2 Euclidean (quantum) field theory. Princeton, New Jersey: Princeton University Press 1974Google Scholar
  4. 4.
    Feldman, J., Osterwalder, K.: The Wightman axioms and the mass gap for weakly coupled (φ4)3 quantum field theories. Ann. Phys.97, 80–135 (1976)Google Scholar
  5. 5.
    Magnen, J., Sénéor, R.: The infinite volume limit of the φ34 model. Ann. Inst. Henri Poincaré24, 95–159 (1976)Google Scholar
  6. 6.
    Fröhlich, J., Simon, B., Spencer, T.: Infrared bounds, phase transitions and continuous symmetry breaking. Commun. math. Phys.50, 79–95 (1976)Google Scholar
  7. 7.
    Park, Y.: Convergence of lattice approximations and infinite volume limit in the (λφ4−σφ2−μφ)3 field theory. J. Math. Phys.18, 354–366 (1977)Google Scholar
  8. 8.
    Feldman, J.: The λφ34 theory in a finite volume. Commun. math. Phys.37, 93–120 (1974); Ph. D. Thesis, Harvard University (1974)Google Scholar
  9. 9.
    Magnen,J.: Thesis, Orsay University (1976)Google Scholar
  10. 10.
    Eckmann, J.-P., Magnen, J., Sénéor, R.: Decay properties and Borel summability for the Schwinger functions inP(φ)2 theories. Commun. math. Phys.39, 251–271 (1975)Google Scholar
  11. 11.
    Dimock, J.: Perturbation expansion for theP(φ)2 quantum field theory. Commun. math. Phys.35, 347–356 (1974)Google Scholar
  12. 12.
    Burnap, C.: The particle structure of Boson quantum field theory models. Thesis, Harvard University (1976)Google Scholar

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • J. Magnen
    • 1
  • R. Sénéor
    • 2
  1. 1.II. Institut für Theoretische PhysikHamburgGermany
  2. 2.Department of PhysicsHarvard UniversityCambridgeUSA

Personalised recommendations