An explicitly solvable model in “Euclidean” field theory: The Fixed Source

  • Abel Klein
Article

Keywords

Field Theory Stochastic Process Probability Theory Mathematical Biology Solvable Model 

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References

  1. 1.
    Albeverrio, S., Krohn, R. Hoegh: Uniqueness of the Physical Vacuum and the Wightman Functions in the Infinite Volume Limit for some Non-Polynomial Interactions. (Comm. Math. Phys. To appear)Google Scholar
  2. 2.
    Gel'fand, I.M., Vilenkin, N.Y.: Les Distributions. Tome 4, Paris: Dunod 1967Google Scholar
  3. 3.
    Glimm, J., Jaffe, A.: Positivity of theϕ 2 3 Hamiltonian. (Fortschr. Physik. To appear)Google Scholar
  4. 4.
    Glimm, J., Jaffe, A., Spencer, T.: The Wightman Axioms for the P(ϕ)2 Quantum Field Models. (Ann. of Math. To appear)Google Scholar
  5. 5.
    Guerra, F., Rosen, L., Simon, B.: The P(ϕ)2 Euclidean Quantum Field Theory as Classical Statistical Mechanics. (Ann. of Math. To appear)Google Scholar
  6. 6.
    Henley, E.M., Thirring, W.: Elementary Quantum Field Theory. New York: McGraw-Hill 1962Google Scholar
  7. 7.
    Nelson, E.: Quantum Fields and Markoff Fields. Proc. Summer Institute of Partial Differential Equations, Berkeley 1971. Providence: Amer. Math. Soc. 1973Google Scholar
  8. 8.
    Nelson, E.: Construction of Quantum Fields from Markoff Fields. J. Functional Analysis 12, 97–112 (1973)Google Scholar
  9. 9.
    Nelson, E.: The Free Markoff Field. J. Functional Analysis 12, 211–227 (1973)Google Scholar
  10. 10.
    Newman, C: The Construction of Stationary Two-Dimensional Markoff Fields with an Application to Quantum Field Theory. (J. Functional Analysis. To appear)Google Scholar
  11. 11.
    Osterwalder, K., Schrader, R.: Axioms for Euclidean Green's Functions. (Comm. Math. Phys. To appear)Google Scholar
  12. 12.
    Schwartz, L.: Théorie des Distributions. Paris: Hermann 1966Google Scholar
  13. 13.
    Schweber, S.: An Introduction to Relativistic Quantum Field Theory. New York: Harper and Row 1961Google Scholar
  14. 14.
    Segal, I.: Tensor Algebras over Hilbert Spaces I. Trans. Amer. Math. Soc, 81, 106–134 (1956)Google Scholar
  15. 15.
    Segal, I.: Distributions in Hilbert Spaces and Canonical Systems of Operators. Trans. Amer. Math. Soc., 88, 12–41 (1958)Google Scholar
  16. 16.
    Segal, I.: Algebraic Integration Theory, Bulletin Amer. Math. Soc., 71, 419–489 (1965)Google Scholar
  17. 17.
    Segal, I.: Nonlinear Functions of Weak Processes. 11. J. Functional Analysis 6, 29–75 (1970)Google Scholar
  18. 18.
    Segal, I.: Introduction to the Mathematical Theory of Quantum Fields. M.I.T. Lecture Notes in Math. Vol. 140, pp. 30–57. Berlin-Heidelberg-New York: 1971Google Scholar
  19. 19.
    Simon, B, Griffiths, R.: The (ϕ 4)2 Field Theory as a Classical Ising Model. (Comm. Math. Phys. To appear)Google Scholar
  20. 20.
    Symanzik, K.: Euclidean Quantum Field Theory I, Equations for a Scalar Model. J. Mathematical Phys. 7, 510–525 (1966)Google Scholar
  21. 21.
    Symanzik, K.: Euclidean Quantum Field Theory, in Local Quantum Theory. Proc. Internat. School Phys. Course 45, R. Jost, Editor. New York: Academic Press 1969Google Scholar
  22. 22.
    Wentzel, G.: Quantum Theory of Fields. New York: Interscience 1949Google Scholar

Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • Abel Klein
    • 1
  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA

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