Abstract
A basic tool in the derivation of multiparticle discontinuity formulae inS-matrix theory is a “structure theorem” which proves analyticity properties for integrals of products of scattering functions [1, 5, 7].
We present here some recent mathematical results and show how they provide directly a general form of this theorem. This new proof, which removes an unnecessary technical assumption of the previous ones, is a development of a method proposed by Pham [8].
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References
Stapp, H.P.: J. Math. Phys.9 (10) 1548 (1968)
Iagolnitzer, D.: Introduction toS-matrix theory. A.D.T. 21 rue Olivier-Noyer 75014 Paris (France) 1973
Iagolnitzer, D., Stapp, H.P.: Commun. math. Phys.14, 15 (1969)
Earlier works on macrocausality are due in particular to Chandler, C., Stapp, H.P.: J. Math. Phys.90, 826 (1969)
Omnes, R.: Phys. Rev.146, 1123 (1966)
Pham, F.: Ann. Inst. Poincaré Vol.6, (2) 89 (1967)
Wanders, G.: Nuov. Cim.14, 168 (1969) and Hels. Phys. Acta38, 142 (1965)
A further discussion of macrocausality is also given in Stapp, H.P.: “Macrocausality and its role in physical theories” and “Foundations ofS-matrix theory” LBL reports, Berkeley
Further results on macrocausality and physical-region analyticity properties are given in [2] and in Iagolnitzer, D.: “Macrocausality, physical-region analyticity and independence property inS-matrix theory”. Saclay preprint (1973), to be published in Proceedings of the Nice 1973 Conference on Hyperfunction Theory and its applications to Theoretical Physics
Coster, J., Stapp, H.P.: J. Math. Phys.10, 371 (1969) and11, 2743 (1969)
Bloxham, M.I.W., Olive, D.I., Polkinghorne, J.C.: J. Math. Phys.10, 494 (1969);10, 545 (1969);10, 553 (1969)
Coster, J., Stapp, H.P.: “Optical theorems for three to three processes”. LBL preprint, Berkeley (1974)
Pham, F.: “Microanalyticité de la matriceS” to be published in Proceeding of the Nice 1973, Conference on Hyperfunction Theory and its applications to Theoretical Physics
The mathematical study of the essential support of a distribution is the result of a collaboration of Bros, J., Iagolnitzer, D. who have developed results of Iagolnitzer, D., Stapp, H.P. [Commun. math. Phys.14, 15 (1969)]. Lemmas 2 and Theorems 1 and 2 of Part I were proved in this last work in a less elaborate form. More elaborate results with various developments, are found in: Bros, J., Iagonitzer, D.: Proceedings of the 1971 Marseille meeting on renormalization theory, and Ann. Inst. H. Poincaré18 (2) 147 (1973)
Bros, J.: In: Proceedings of the November 1971 Strasbourg meeting of RCP 25
Iagolnitzer, D.: Ref. [2], Chapter II-C and Appendix I, and “Essential support of a distribution-An introduction” Saclay preprint 1973, to be published in Proceedings of the 1973 Nice conference on Hyperfunction Theory and its applications to theoretical Physics
All decomposition theorems of Part I (in terms of hyperfunctions), including Theorem 3, are also consequences of the general results of Ref. [10] below obtained independently in the framework of hyperfunction theory, with a different definition of the essential support, called “singular spectrum”. A new proof of Theorem 3 (in terms of distributions) is given in Ref. [11] below
Sato, M., Kawai, T., Kashiwara, M.: In: Hyperfunctions and Pseudo. Differential Equations. Proceeding of the 1971 Katata Conference, Lectures Notes in Mathematics287, Berlin-Heidelberg-New York: Springer 1973
An account of the results concerning the singular spectrum, the decomposition theorems and theorems on products and integrals is given in Cerezo, Chazarain, Piriou, to be published in Proceedings of the Nice 1973 Confeence on Hyperfunction Theory and its Applications to Theoretical Physics
Bros, J., Iagolnitzer, D.: In preparation
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Communicated by R. Haag
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Iagolnitzer, D. The structure theorem inS-matrix theory. Commun.Math. Phys. 41, 39–53 (1975). https://doi.org/10.1007/BF01608546
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DOI: https://doi.org/10.1007/BF01608546