Skip to main content
Log in

Axioms for Euclidean Green's functions

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

We establish necessary and sufficient conditions for Euclidean Green's functions to define a unique Wightman field theory.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Borchers, H. J.: On structure of the algebra of field operators. Nuovo Cimento24, 214 (1962).

    Google Scholar 

  2. Dimock, J., Glimm, J.: Measures on the Schwartz distribution space and applications to quantum field theory (to appear).

  3. Dyson, F. J.: TheS matrix in quantum electrodynamics. Phys. Rev.75, 1736 (1949).

    Google Scholar 

  4. Feldman, J.: A relativistic Feynman-Kac formula. Harvard preprint (1972).

  5. Gelfand, I. M., Shilov, G. E.: Generalized functions, Vol. 2. New York: Academic Press 1964.

    Google Scholar 

  6. Glimm, J., Jaffe, A.: Quantum field theory models, in the 1970 Les Houches lectures. Dewitt, C., Stora, R. (Ed.). New York: Gordon and Breach Science Publishers 1971.

    Google Scholar 

  7. Glimm, J., Jaffe, A.: Positivity of the ϕ 43 Hamiltonian, preprint 1972.

  8. Glimm, J., Jaffe, A.: The λϕ 42 quantum field theory without cutoffs IV. J. Math. Phys.13, 1568 (1972).

    Google Scholar 

  9. Glimm, J., Spencer, T.: The Wightman axioms and the mass gap for theP (ϕ)2 quantum field theory, preprint (1972).

  10. Hall, D., Wightman, A. S.: A theorem on invariant analytic functions with applications to relativistic quantum field theory. Mat.-Fys. Medd. Danske Vid. Selsk.31, No. 5 (1951).

    Google Scholar 

  11. Hörmander, L.: On the division of distributions by polynomials. Arkiv Mat.3, 555 (1958).

    Google Scholar 

  12. Jost, R.: The general theory of quantized fields. Amer. Math. Soc. Publ., Providence R. I., 1965.

  13. Jost, R.: Eine Bemerkung zum CTP-Theorem. Helv. Phys. Acta30, 409 (1957).

    Google Scholar 

  14. Jost, R.: Das Pauli-Prinzip und die Lorentz-Gruppe. In: Theoretical physics in the twentieth century, ed. Fierz, M., Weisskopf, V. New York: Interscience Publ. 1960.

    Google Scholar 

  15. Nelson, E.: Quantum fields and Markoff fields. Amer. Math. Soc. Summer Institute on PDE, held at Berkeley, 1971.

  16. Nelson, E.: Construction of quantum fields from Markoff fields, preprint (1972).

  17. Nelson, E.: The free Markoff field, preprint (1972).

  18. Osterwalder, K., Schrader, R.: Euclidean Fermi fields and a Feynman-Kac formula for Boson-Fermion models, Helv. Phys. Acta, to appear, and Phys. Rev. Lett.29, 1423 (1972).

    Google Scholar 

  19. Robertson, A. P., Robertson, W. J.: Topological vector spaces. London and New York: Cambridge Univ. Press 1964.

    Google Scholar 

  20. Ruelle, D.: Connection between Wightman functions and Green functions inP-space. Nuovo Cimento19, 356 (1961).

    Google Scholar 

  21. Schwinger, J.: On the Euclidean structure of relativistic field theory. Proc. Natl. Acad. Sci. U.S.44, 956 (1958).

    Google Scholar 

  22. Schwinger, J.: Euclidean quantum electrodynamics. Phys. Rev.115, 721 (1959).

    Google Scholar 

  23. Streater, R. F., Wightman, A. S.: PCT, spin and statistics and all that. New York: Benjamin 1964.

    Google Scholar 

  24. Symanzik, K.: Euclidean quantum field theory. I. Equations for a scalar model. J. Math. Phys.7, 510 (1966).

    Google Scholar 

  25. Symanzik, K.: Euclidean quantum field theory. In: Proceedings of the International School of Physics “ENRICO FERMI”, Varenna Course XLV, ed. Jost, R. New York: Academic Press 1969.

    Google Scholar 

  26. Vladimirov, V. S.: Methods of the theory of functions of several complex variables. Cambridge and London: MIT Press 1966.

    Google Scholar 

  27. Whitney, H.: Analytic extensions of differentiable functions defined in closed sets. Trans. Amer. Math. Soc.36, 63 (1934).

    Google Scholar 

  28. Wightman, A. S.: Quantum field theory and analytic functions of several complex variables. J. Indian Math. Soc.24, 625 (1960).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Supported by the National Science Foundation under grant GP 31239X.

Supported in part by the Air Force Office of Scientific Research, contract AF 44620-70-C-0030.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Osterwalder, K., Schrader, R. Axioms for Euclidean Green's functions. Commun.Math. Phys. 31, 83–112 (1973). https://doi.org/10.1007/BF01645738

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01645738

Keywords

Navigation