Skip to main content
Log in

On the connection between analyticity and lorentz covariance of wightman functions

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

Abstract

We prove a conjecture ofR. Streater [1] on the finite covariance of functions holomorphic in the extended tube which are Laplace transforms of two tempered distributions with supports in the future and past cones. A new, slightly more general proof is given for a theorem of analytic completion of [1].

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. Streater, R. F.: J. Math. Phys.3, 256 (1962).

    Google Scholar 

  2. ——, andA. S. Wightman: PCT, spin and statistics and all that. New York: Benjamin 1964. Definition of Jost points: p. 70.

    Google Scholar 

  3. Bogoliubov, N. N., iV. S. Vladimirov: Nauchn. Dokl. Vysshei Shkoly3, 26 (1958).

    Google Scholar 

  4. Borchers, H. J.: Nuovo Cimento24, 214 (1961).

    Google Scholar 

  5. This can be extracted from:L. K. Hua, Harmonic analysis of functions of several complex variables in classical domains. Providence R. I.: American Mathematical Society 1963. A direct proof can also be made using the Peter-Weyl Theorem and a trick due toS. Bergman.

  6. Schwartz, L.: Medd. Lunds Mat. Sem. Supplementband p. 196 (1952).

  7. Gårding, L., andJ. L. Lions: Nuovo Cimento Suppl.14, 9 (1959).

    Google Scholar 

  8. Vladimirov, V. S.: Tr. Mat. Inst. Akad. Nauk SSSR,60, 101–144 (1961).

    Google Scholar 

  9. Wightman, A. S.: In: Relations de dispersion et particules élémentaires,DeWitt andOmnès, ed. Paris: Hermann 1960.

    Google Scholar 

  10. Zerner, M.: Les fonctions holomorphes à valeurs vectorielles et leurs valeurs au bord. Unpublished lecture notes, Orsay 1961.

  11. Gårding, L., andA. S. Wightman: Unpublished. We are grateful to ProfessorA. S. Wightman for kindly showing us the manuscript of this work.

  12. Schwartz, L.: Théorie des distributions. Paris: Hermann 1957–1959.

    Google Scholar 

  13. Vladimirov, V. S.: Tr. Mat. Inst. Akad. Nauk SSSR64, 9 (1961).

    Google Scholar 

  14. See, for instance,F. Bruhat: Lectures on Lie groups and representations of locally compact groups. Tata Institute for Fundamental Research. Bombay 1958.

  15. See, for instance,E. Wichmann: Lecture Notes, Copenhagen University and Nordita 1962.

  16. Weyl, H.: The theory of groups and quantum mechanics, p. 153. New York: Dover Publications, Inc. 1931.

    Google Scholar 

  17. Hepp, K.: Helv. Phys. Acta36, 355 (1963).

    Google Scholar 

  18. Steinmann, O.: Helv. Phys. Acta33, 257 (1960).

    Google Scholar 

  19. Ruelle, D.: Nuovo Cimento19, 356 (1951).

    Google Scholar 

  20. Araki, H., andN. Burgoyne: Nuovo Cimento18, 342 (1960).

    Google Scholar 

  21. Araki, H.: J. Math. Phys.2, 163 (1961).

    Google Scholar 

  22. Steinmann, O.: Helv. Phys. Acta36, 90 (1963).

    Google Scholar 

  23. Jost, R.: The general theory of quantized fields. American Mathematical Society 1965.

  24. Ruelle, D.: Private communication.

  25. Bros, J.: Séminaire Lelong (1962), No. 8. Paris 1962.

  26. Bremermann, H.: Thesis, Schrift. Math. Inst. Univ. Münster, No. 5 (1951). See also ref. [27].

  27. Vladimirov, V. S.: Metody teorii mnogikh complexnykh peremennykh. Moscow: Izd. Nauka 1964.

    Google Scholar 

  28. Rossi, H.: Global theory of several complex variables. Lectures at Princeton University, p. 77 (1961). A Riemann domain is a generalization of a Riemann surface to the case of more than one complex variable.

  29. Ahlfors, L., andL. Sario: Riemann surfaces, p. 30. Princeton: Princeton University Press 1960.

    Google Scholar 

  30. Hall, D., ogA. Wightman: Mat. Fys. Med. Kon. Dan. Vid. Selskab31, No. 5 (1957).

  31. Jost, R.: In: Field theory and the many-body problem.E. Caianiello, ed. New York: Academic Press 1961.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bros, J., Epstein, H. & Glaser, V. On the connection between analyticity and lorentz covariance of wightman functions. Commun.Math. Phys. 6, 77–100 (1967). https://doi.org/10.1007/BF01654126

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01654126

Keywords

Navigation