Communications in Mathematical Physics

, Volume 109, Issue 3, pp 437–480 | Cite as

Construction and Borel summability of infrared Φ44 by a phase space expansion

  • J. Feldman
  • J. Magnen
  • V. Rivasseau
  • R. Sénéor


We construct the thermodynamic limit of the critical (massless) φ4 model in 4 dimensions with an ultraviolet cutoff by means of a “partly renormalized” phase space expansion. This expansion requires in a natural way the introduction of effective or “running” constants, and the infrared asymptotic freedom of the model, i.e. the decay of the running coupling constant, plays a crucial rôle. We prove also that the correlation functions of the model are the Borel sums of their perturbation expansion.


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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • J. Feldman
    • 1
  • J. Magnen
    • 1
  • V. Rivasseau
    • 1
  • R. Sénéor
    • 1
  1. 1.Centre de Physique ThéoriqueEcole PolytechniquePalaiseau CedexFrance

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