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An Asymptotic Perturbation Expansion for Multiphase \( \varphi _2^4 \cdot \)

  • Arthur Jaffe
  • James Glimm
  • Thomas Spencer
Conference paper
Part of the Acta Physica Austriaca book series (FEWBODY, volume 16/1976)

Abstract

We consider the d=2 quantum field, with interaction density \( P\left( x \right) = \lambda x^4 - \frac{3} {4}x^2 . \) for λ < < 1, this model is known to have a phase transition [1], i.e. there exist at least two different field theories for a given λ. The new result we announce here is a detailed investigation of the two theories in which ⌽ is concentrated near ± (8λ)-1/2, namely the global minima of P(x). (Presumably these are the only pure states for the model.) We give a convergent expansion about the mean field approximation, which is asymptotic in powers of λ1/2. We explain these ideas in more detail.

Keywords

Gaussian Measure Cluster Expansion Path Space Interaction Density Convergent Expansion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    J. Glimm, A. Jaffe and T. Spencer, Phase Transitions for Quantum Fields, Commun. Math. Phys. 45, 203–216 (1975).MathSciNetADSCrossRefGoogle Scholar
  2. J. Glimm, A. Jaffe and T. Spencer, Existence of Phase Transitions for Quantum Fields, Proc. of the Colloq. on Mathematical Methods of Quantum Field Theory, Marseille, June 1975.Google Scholar
  3. 2.
    J. Glimm, A. Jaffe and T. Spencer, A Convergent Expansion about Mean Field Theory: I. The Expansion. II. Convergence of the Expansion, to appear.Google Scholar
  4. 3.
    J. Glimm, A. Jaffe and T. Spencer, The Wightman Axioms and Particle Structure in the P(⌽)2 Quantum Field Model, Ann. Math. 100, 585–632 (1974).MathSciNetCrossRefGoogle Scholar
  5. J. Glimm, A. Jaffe and T. Spencer, The Particle Structure of the Weakly Coupled P(⌽)2 Model and other Applications of High Temperature Expansions. Part II: The Cluster Expansion. In “Constructive Quantum Field Theory”, G. Velo and A. Wightman (eds.) Springer Lecture Notes in Physics, Volume 25, Heidelberg 1973.Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • Arthur Jaffe
    • 1
  • James Glimm
    • 2
  • Thomas Spencer
    • 3
  1. 1.Harvard UniversityCambridgeUSA
  2. 2.Rockefeller UniversityNew YorkUSA
  3. 3.Rockefeller UniversityNew YorkUSA

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