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Analyticity properties and many-particle structure in general quantum field theory

II. One-particle irreduciblen-point functions

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Abstract

The extraction of one-particle singularities from then-point functions is performed in the framework of L.S.Z. field theory in the case of a single massive scalar field. It is proved that the “one-particle irreducible” functions thus obtained enjoy the analytic and algebraic primitive structure of generaln-point functions (up to a finite number of generalized C.D.D. singularities). Finally under an additional technical assumption, it is shown that the Glaser-Lehmann-Zimmermann relations stating the completeness of asymptotic states yield similar relations satisfied in any given channel by the corresponding one-particle irreducible functions.

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References

  1. Lassalle, M.: Commun. math. Phys.36, 185 (1974)

    Article  MathSciNet  Google Scholar 

  2. Bros, J.: Analytic methods in mathematical physics. New York: Gordon and Breach 1970

    Google Scholar 

  3. Symanzik, K.: J. Math. Phys.1, 249 (1960) and in Symposium on theoretical physics, Vol.3. New York: Plenum Press 1967

    Article  MathSciNet  Google Scholar 

  4. Zimmermann, W.: Nuovo Cimento13, 503 (1959);16, 690 (1960)

    MATH  Google Scholar 

  5. Lehmann, H., Symanzik, K., Zimmermann, W.: Nuovo Cimento1, 205 (1955);6, 319 (1957)

    MathSciNet  Google Scholar 

  6. Hepp, K.: Commun. math. Phys.1, 95 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  7. Steinmann, O.: Commun. math. Phys.10, 245 (1968)

    Article  MATH  MathSciNet  Google Scholar 

  8. Glaser, V., Lehmann, H., Zimmermann, W.: Nuovo Cimento6, 1122 (1957)

    MathSciNet  Google Scholar 

  9. Völkel, A.H.: Commun. math. Phys.2, 176 (1966)

    Article  Google Scholar 

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

    Google Scholar 

  11. Jost, R.: The general theory of quantized fields. Am. Math. Soc. Providence 1965

  12. Castillejo, L., Dalitz, R., Dyson, F. J.: Phys. Rev.101, 453 (1966)

    ADS  Google Scholar 

  13. Haag, R.: Phys. Rev.112, 669 (1958)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  14. Ruelle, D.: Helv. Phys. Acta35, 147 (1962)

    MATH  MathSciNet  Google Scholar 

  15. Martin, A.: In: Problems of theoretical physics, p. 113. Moscow: Bauka 1969

    Google Scholar 

  16. Bros, J., Epstein, H., Glaser, V., Stora, R.: To appear

  17. Epstein, H., Glaser, V., Stora, R.: Cern preprint TH. 1719 (1973)

  18. Steinmann, O.: Helv. Phys. Acta33, 257, 347 (1960)

    MATH  MathSciNet  Google Scholar 

  19. Bros, J.: Thesis (Paris 1970)

  20. Lassalle, M.: Thesis (Orsay 1975)

  21. Ruelle, D.: Nuovo Cimento19, 356 (1961)

    MATH  MathSciNet  Google Scholar 

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

    MathSciNet  Google Scholar 

  23. Pohlmeyer, K.: Report Desy 66/36 (unpublished), Hamburg (1966)

  24. Bros, J., Lassalle, M.: III. Two-particle irreducibility properties (to appear)

  25. Titchmarsh, E.C.: Theory of Fourier integrals, p. 145. Oxford: Clarendon Press 1959

    Google Scholar 

  26. Courant, R., Hilbert, D.: Methods of mathematical physics, Vol. II, p. 248. New York: Interscience Publ. 1962

    Google Scholar 

  27. Bros, J., Epstein, H., Glaser, V.: Helv. Phys. Acta45, 149 (1972); see also Bros, J., Iagolnitzer, D. In: Proceedings of the International Moscow 1972 Conference on Quantum Field Theory and Quantum Statistics

    Google Scholar 

  28. Schwartz, L.: Théorie des distributions. Paris: Hermann 1959

    Google Scholar 

  29. Bros, J., Iagolnitzer, D.: Ann. Inst. Henri Poincaré, vol. XVIII n0 2, 147 (1973) and Essential supports and local analytic structure of distributions (to appear)

    MathSciNet  Google Scholar 

  30. Williams, D.N.: Lectures in Theoretical Physics, Vol.10. B, 357 (1967)

    Google Scholar 

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Authors and Affiliations

  1. Service de Physique Théorique, Centre d'Études Nucléaires de Saclay, Gif-sur-Yvette, France

    J. Bros

  2. Centre de Physique Théorique, Ecole Polytechnique, Paris, France

    M. Lassalle

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  1. J. Bros
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  2. M. Lassalle
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Communicated by R. Haag

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Bros, J., Lassalle, M. Analyticity properties and many-particle structure in general quantum field theory. Commun.Math. Phys. 43, 279–309 (1975). https://doi.org/10.1007/BF02345025

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