Abstract
The monodromy rings of Feynman integrals for one loop graphs with an arbitrary number of lines are determined.
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Ponzano, G., Regge, T., Speer, E. R., Westwater, M. J.: Commun. Math. Phys.15, 83–132 (1969).
Ponzano, G., Regge, T.: The Monodromy Group of One-Loop Relativistic Feynman Integrals. Published in a volume on the occasion of the 60th birthday of the academician N. N. Bogoliubov.
Speer, E. R.: Generalized Feynman Amplitudes. Princeton, N. J.: Princeton University Press 1969.
Regge, T.: The Fundamental Group of Poincaré and the Analytic Properties of Feynman Relativistic Amplitudes. Nobel Symposium 8; Elementary Particle Theory, ed. Nils Svartholm. New York: Interscience 1969.
Eden, R. J., Landshoff, P. V., Olive, D. I., Polkinghorne, J. C.: The Analytic-S-Matrix. Cambridge: Cambridge University Press 1966.
Regge, T.: Algebraic Topology Methods in the Theory of Feynman Relativistic Amplitudes. Battelle Rencontres, 1967. Lectures in Mathematics and Physics, ed. C. M. DeWitt, J. A. Wheeler. New York: W. A. Benjamin 1968.
Halmos, P. R.: Finite Dimensional Vector Spaces. Princeton, N. Y.: Princeton University Press 1962.
Byers, N., Yang, C. N.: Rev. Mod. Phys.36, 595 (1964).
van der Waerden, B. L.: Modern Algebra, Vol. II. New York: Fredrick Ungar Publishing Co. 1948.
Pham, F.: Introduction à l'Étude Topologique des Singularités de Landau. Paris: Gauthier-Villars 1967.
Westwater, M. J.: Structure of Feynman Functions. Thesis, Cambridge, 1966.
Plemelj, J.: Problems in the Sense of Riemann and Klein. Interscience Tracts in Mathematics16, 1964.
Schläfli, L. Theorie der vielfachen Kontinuität. Berne 1852; Ges. Math. Abh I. Basel 1950 (p. 209).
Polyà, G.: Induction and Analogy in Mathematics. Princeton, N.J.: Princeton University Press, 1954 (p. 43).
Boyling, J. B.: Nuovo Cimento53, 351–375 (1968).
Fotiadi, D., Froissart, M., Lascoux, J., Pham, F.: Topology4, 159–191 (1965). Reprinted in Homology and Feynman Integrals, R. C. Hwa and V. L. Teplitz. New York: W. A. Benjamin 1966.
Hironaka, H.: Ann. Math.79, 109–326 (1964).
Fotiadi, D.: Désingularisation et Graphes de Feynman. Séminaire, Collège de France, 1969.
—— Pham, F.: Analytic Study of Some Feynman Graphs by Homological Methods. Reprinted in Homology and Feynman Integrals, R. C. Hwa and V. L. Teplitz. New York: W. A. Benjamin 1966.
Garside, F. A.: Quart. J. Math. Oxford (2)20, 235–254 (1969).
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Research sponsored by the National Science Foundation, Grant No. GP-16147.
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Ponzano, G., Regge, T., Speer, E.R. et al. The monodromy rings of one loop Feynman integrals. Commun.Math. Phys. 18, 1–64 (1970). https://doi.org/10.1007/BF01649638
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DOI: https://doi.org/10.1007/BF01649638