Advertisement

Communications in Mathematical Physics

, Volume 35, Issue 4, pp 347–356 | Cite as

Asymptotic perturbation expansion in theP(φ)2 quantum field theory

  • Jonathan Dimock
Article

Abstract

In theP(φ)2 model it is proved that the perturbation series for the infinite volume Schwinger functionsS(λ) are asymptotic in the limit as the coupling constant λ goes to zero. We also give conditions which imply smoothness ofS(λ) at arbitrary λ.

Keywords

Neural Network Statistical Physic Field Theory Complex System Quantum Field Theory 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Dimock, J., Glimm, J.: Measures on Schwartz Distribution Space and Applications toP(φ)2 Field Theories, to appear in Adv. Math.Google Scholar
  2. 2.
    Glimm, J., Jaffe, A., Spencer, T.: The Wightman axioms and Particle Structure in theP(φ)2 Quantum Field Model, to appearGoogle Scholar
  3. 3.
    Glimm, J., Spencer, T.: The Wightman Axioms and the Mass Gap for theP(φ)2 Quantum Field Theory, preprintGoogle Scholar
  4. 4.
    Guerra, F., Rosen, L., Simon, B.: TheP(φ)2 Quantum Field Theory as Classical Statistical Mechanics, preprintGoogle Scholar
  5. 5.
    Hepp, K.: On the Connection between Wightman and LSZ Quantum Field Theory. In: Cretien, M., Deser, S. (Eds.): Axiomatic Field Theory. New York: Gordon and Breach 1966Google Scholar
  6. 6.
    Jaffe, A.: Divergence of Perturbation Theory for Bosons. Commun. math. Phys.1, 127–149 (1965)Google Scholar
  7. 7.
    Jost, R.: The General Theory of Quantized Fields. Am. Math. Soc., Providence (1965)Google Scholar
  8. 8.
    Lebowitz, J.: Bounds on the Correlations and Analyticity Properties of Ferromagnetic Ising Spin Systems. Commun. math. Phys.28, 313–321 (1972)Google Scholar
  9. 9.
    Nelson, E.: Construction of Quantum Fields from Markov Fields. J. Funct. Anal.12, 97–112 (1973)Google Scholar
  10. 10.
    Nelson, E.: The Free Markov Field. J. Funct. Anal.12, 211–227 (1973)Google Scholar
  11. 11.
    Osterwalder, K., Schrader, R.: Axioms for Euclidean Green's Functions. Commun. math. Phys.31, 83–112 (1973)Google Scholar
  12. 12.
    Simon, B.: In: Proc. Coral Gables Conference, 1972, to appearGoogle Scholar
  13. 13.
    Simon, B., Griffiths, R.: The (φ4)2 Field Theory as a Classical Ising Model, preprintGoogle Scholar
  14. 14.
    Symanzik, K.: Euclidean Quantum Field Theory. In: Jost, R. (Ed.): Local Quantum Theory. New York: Academic Press 1969Google Scholar

Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • Jonathan Dimock
    • 1
    • 2
  1. 1.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA
  2. 2.Department of MathematicsState University of New York at BuffaloAmherstUSA

Personalised recommendations