Advertisement

Probability theory and euclidean field theory

  • Edward Nelson
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 25)

Keywords

Probability Space Gaussian Random Variable Real Hilbert Space Reflection Property Logarithmic Sobolev Inequality 
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]
    R. L. Dobrushin and R. A. Minlos, Construction of a one-dimensional quantum field via a continuous Markoff field, submitted to Functional Analysis and its Applications.Google Scholar
  2. [2]
    J. Ginibre, General formulation of Griffiths’ inequalities, Communications in Math. Phys. 16 (1970), 310–328.CrossRefADSMathSciNetGoogle Scholar
  3. [3]
    J. Glimm, Boson fields with nonlinear self-interaction in two dimensions, Communications in Math. Phys. 8 (1968), 12–25.zbMATHCrossRefADSGoogle Scholar
  4. [4]
    Robert B. Griffiths, Rigorous results for Ising ferromagnets of arbitrary spin, J. of Mathematical Physics 10 (1969), 1559–1565.CrossRefADSGoogle Scholar
  5. [5]
    Robert B. Griffiths, Phase transitions, in Statistical Mechanics and Quantum Field Theory (Les Houches 1970) ed. C. DeWitt and R. Stora, Gordon and Breach, New York (1971), 241–279.Google Scholar
  6. [6]
    Leonard Gross, Logarithmic Sobolev Inequalities, Cornell University preprint (1973).Google Scholar
  7. [7]
    F. Guerra, L. Rosen, and B. Simon, The P(ϕ)2 Euclidean quantum field theory as classical statistical mechanics, to appear in Annals of Mathematics.Google Scholar
  8. [8]
    P. R. Halmos, Normal dilations and extensions of operators, Summa Brasiliensis Math. 2 (1950), 125–134.MathSciNetGoogle Scholar
  9. [9]
    Edward Nelson, The free Markoff field, J. Functional Anal. 12 (1973), 211–227.zbMATHCrossRefGoogle Scholar
  10. [10]
    Edward Nelson, Construction of quantum fields from Markoff fields, J. Functional Anal. 12 (1973), 97–112.zbMATHCrossRefGoogle Scholar
  11. [11]
    K. Osterwalder and R. Schrader, Axioms for Euclidean Green’s functions, Communications in Math. Phys. 31, 83 (1973).zbMATHCrossRefADSMathSciNetGoogle Scholar
  12. [12]
    Shôichirô Sakai, C*-Algebras and W*-Algebras, Ergebnisse der Math. und ihrer Grenzgebiete, Band 60, Springer-Verlag, New York, 1971.Google Scholar
  13. [13]
    I. E. Segal, Tensor algebras over Hilbert spaces, Trans. Amer. Math. Soc. 81 (1956), 106–134.zbMATHCrossRefMathSciNetGoogle Scholar
  14. [14]
    Elias M. Stein and Guido Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton (1971).zbMATHGoogle Scholar
  15. [15]
    K. Symanzik, Euclidean quantum field theory, Rend. Scuola Int. Fis. E. Fermi, XLV Corso.Google Scholar
  16. [16]
    G. Szegő, Orthogonal Polynomials, Amer. Math. Soc. Coll. Publ. XXIII, New York (1939).Google Scholar

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • Edward Nelson
    • 1
  1. 1.Department of MathematicsPrinceton UniversityUSA

Personalised recommendations