Abstract
A tentative review of recent results obtained by several authors will be presented. They mainly concern the derivation of analyticity properties for the Green's functions and collision amplitudes of the 2 → 2, 2 → 3, 3 → 3-particle processes from the general principles of Q.F.T. ; emphasis will be laid on the exploitation of asymptotic completeness which generates the monodromic structure of Green's functions. In this connection, the role played by “generalized Bethe-Salpeter kernels” will be described.
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References
G.F. CHEW, The Analytic S-Matrix, W.A. Benjamin, New York (1966) and references quoted therein.
D. IAGOLNITZER, The S-matrix, North Holland, Amsterdam (1978) and references quoted therein.
J.P. ECKMANN, H.EPSTEIN, Comm. Math. Phys., 64, 95 (1979).
S.M. ROY, G. WANDERS, Physics Letters, 74B, 347 (1978) and Nucl. Phys. B141, 220 (1978).
A.A. LOGUNOV et al., Theor. Math. Phys. 33, 149 (1977).
L.M. MUSAFAROV, Theor. Math. Phys. 38, 36 (1979).
V.P. PAVLOV, Theor. Math. Phys. 37, 154 (1978).
V.P. PAVLOV, Theor. Math. Phys. 35, 3 (1978).
L.M. MUSAFAROV, V.P. PAVLOV, Theor. Math. Phys. 35, 151 (1978).
L.M. MUSAFAROV, Theor. Math. Phys. 35, 291 (1978).
H. EPSTEIN, V. GLASER, D. IAGOLNITZER,in preparation.
J. BROS in “Analytic Methods in Math. Physics”, p.85, Gordon and Breach, New York (1970).
K. SYMANZIK, J. Math. Phys. 1, 249 (1960).
K. SYMANZIK, in Symposium on Theoretical Physics, 3, New York, Plenum Press (1967).
R.F. STREATER and A.S. WIGHTMAN, “PCT, Spin & Statistics and all that”, Benjamin, New York (1964).
R. JOST, “The general theory of quantized fields”, Ann. Math. Soc. Providence R.I. (1965).
K. OSTERWALDER, R. SCHRADER, Comm. Math. Phys. 33, 83 (1973) and 42, 281 (1975).
V. GLASER, Comm. Math. Phys. 37, 257 (1974).
J. GLIMM, A. JAFFE, T. SPENCER, Ann. Math. 100, 585 (1974).
See [3] and references quoted therein.
O. STEINMANN, Comm. Math. Phys. 10, 245 (1968).
H. EPSTEIN, V. GLASER, R. STORA, “Structural Analysis of Collision Amplitudes”, p.7, North-Holland, Amsterdam (1976) and references quoted therein.
K. HEPP in: “Axiomatic Field Theory”, Gordon and Breach, New-York (1966).
T. SPENCER and F. ZIRILLI, Comm. Math. Phys. 49, 1 (1975).
D. RUELLE, Nuovo Cimento 19, 356 (y) and Thesis, Zurich (1959).
See R. JOST [9 b] and references quoted therein.
J. BROS, H. EPSTEIN, V. GLASER, Nuovo Cim. 31, 1265 (1964)
J. BROS, H. EPSTEIN, V. GLASER, Comm. Math. Phys. 1, 240 (1965)
J. BROS, H. EPSTEIN, V. GLASER Helv. Phys. Acta. 45, 149 (1972).
A. MARTIN: Nuovo Cimento, 42 A 930 (1966) and 44 1219 (1966).
A. MARTIN, “Scattering theory: unitarity analyticity and crossing”, Springer-Verlag (1970).
H. EPSTEIN, J. Math. Phys. 1 254 (1960).
J. BROS, b) D. IAGOLNITZER in Publ. R.I.M.S., Kyoto Univ. 12 Suppl. (1976).
M. SATO, T. KAWAI, M. KASHIWARA, Lect. Notes in Math., Springer Verlag (1972).
A.S.WIGHTMAN, in “Relations de dispersion ...” Hermann, Paris (1960), ref.therein.
J. BROS, V. GLASER, l'enveloppe d'holomorphie de l'union de deux polycercles. (1961)
M.C. POLIVANOV, “Math.Pb. in Math.Phys.”,375 Lect. Notes in Phys.,Springer (197).
N.N. BOGOLIUBOV, D.V. SHIRKOV, “Intr, to the theory, of Quantized Fields”, Moscow
J. BROS, M. LASSALLE, Comm. Math. Phys. 43, 279 (1975). (1957).
J. BROS, M. LASSALLE, Comm. Math. Phys. 54, 33 (1977).
W. ZIMMERMANN, Nuovo Cimento, 21 249 (1961)
A. MARTIN, in “Problems of Theoretical Physics”, Moscow, Bauka (1969).
J. BROS and D. PESENTI, “Fredholm theory in complex manifolds” to be published in “Journal de Math. Pures et Appliquées”. (preprint Orsay 1979).
J. BROS, Cours de Sème cycle, Lausanne, Mai 1979.
R. ASCOLI, Nuovo Cimento, 18 754 (1960)
J. BROS, M. LASSALLE, “Structural Analysis of Collision Amplitudes”, p.97, North-Holland, Amsterdam (1976).
A. KATZ, Thèse de 3ème cycle Paris, Juin 1979.
M. LASSALLE, Comm. Math. Phys. 34, 185 (1974).
J. BROS, M. GRAMMATICOU, “Renormalized g-convolution I”, Saclay (1978) to be published in Comm. Math. Phys
M. GRAMMATICOU, “Renormalized convolution II”, Ecole Polytechnique,Paris 1979.
W. ZIMMERMANN, Comm. Math. Phy 15, 208 (1969).
S. WEINBERG, Phys. Rev. 118 (1960).
J. BROS and D. PESENTI, in preparation.
G. SOMMER, in preparation.
R. OMNES, in “Relations de dispersion ...” Hermann, Paris (1960), ref. therein.
F. DUNLOP, M. COMBESCURE, n-particle irreducible functions in euclidean O.F.T. Preprint IHES (1978), and H. KOCH, Thesis, Genève (1979).
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Bros, J. (1980). Analytic structure of Green's functions in quantum field theory. In: Osterwalder, K. (eds) Mathematical Problems in Theoretical Physics. Lecture Notes in Physics, vol 116. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09964-6_319
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DOI: https://doi.org/10.1007/3-540-09964-6_319
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