On the evaluation of one-loop Feynman amplitudes in euclidean quantum field theory
Ortner, N. ; Wagner, P.
Annales de l'I.H.P. Physique théorique, Tome 63 (1995), p. 81-110 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1995-01-01
@article{AIHPA_1995__63_1_81_0,
     author = {Ortner, N. and Wagner, P.},
     title = {On the evaluation of one-loop Feynman amplitudes in euclidean quantum field theory},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {63},
     year = {1995},
     pages = {81-110},
     mrnumber = {1354440},
     zbl = {0835.46042},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1995__63_1_81_0}
}

Ortner, N.; Wagner, P. On the evaluation of one-loop Feynman amplitudes in euclidean quantum field theory. Annales de l'I.H.P. Physique théorique, Tome 63 (1995) pp. 81-110. http://gdmltest.u-ga.fr/item/AIHPA_1995__63_1_81_0/

[1] J.D. Bjorken and S.D. Drell, Relativistic Quantum Fields, McGraw Hill, New York, 1965. | MR 187642 | Zbl 0184.54201

[2] J. Böhm, Untersuchung des Simplexinhaltes in Raumen konstanter Krümmung beliebiger Dimension, J. Reine Angew. Math., vol. 202, 1959, pp. 16-51. | MR 121712 | Zbl 0088.13203

[3] J. Böhm, Inhaltsmessung im R5 konstanter Krümmung, Arch. Math., vol. 11, 1960, pp. 298-309. | MR 121714 | Zbl 0095.15203

[4] J. Böhm and Ei. Hertel, Polyedergeometrie in n-dimensionalen Räumen konstanter Krümmung, Birkhäuser Verlag, Basel, 1981. | MR 626823 | Zbl 0466.52001

[5] B.C. Carlson, Special Functions of Applied Mathematics, Academic Press, New York, 1977. | MR 590943 | Zbl 0394.33001

[6] H.S.M. Coxeter, The functions of Schläfli and Lobatschefsky, Quarterly J. Math. Oxford, vol. 6, 1935, pp. 13-29. | Zbl 0011.17006

[7] D.K. Faddeev and W.N. Faddeeva, Computational Methods of Linear Algebra, Freeman, San Francisco, 1963. | MR 158519

[8] R.P. Feynman, The theory of positrons, Phys. Rev., (2), vol. 76, 1949, pp. 749-759. | Zbl 0037.12406

[9] R.P. Feynman, Space-time approach to quantum electrodynamics, Phys. Rev., (2), vol. 76, 1949, pp. 769-789. | MR 35687 | Zbl 0038.13302

[10] R.P. Feynman, Quanten-Elektrodynamik, B. I. - Hochschultaschenbuch 401, Bibliographisches Institut, Mannheim, 1969. | Zbl 0172.56604

[11] I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products, 4th ed., 6th printing, Academic Press, New York, 1972.

[12] W. Gröbner, Matrizenrechnung, B.I. - Hochschultaschenbuch 103/103a, Bibliographisches Institut, Mannheim, 1966. | MR 199199 | Zbl 0168.02202

[13] W. Gröbner and N. Hofreiter, Integraltafel, II. Teil: Bestimmte Integrale, 5. Aufl., Springer, Wien, 1973. | Zbl 0298.65016

[14] G.H. Hardy, Notes on some points in the integral calculus XI, Messenger of Math., vol. 32, 1903, pp. 159-165, in Collected Papers, Vol. V, At the Clarendon Press, Oxford, 1972, pp. 332-339. | JFM 33.0313.02

[15] H. Holmann, Lineare und multilineare Algebra, B. I. - Hochschultaschenbuch 173/173a*, Bibliographisches Institut, Mannheim, 1970. | MR 320019 | Zbl 0217.05402

[16] H. Hopf, Die curvatura integra Clifford-Kleinscher Raumformen, Nachr. Ges. Wiss. Göttingen Math.-phys. Kl. 1925, 1926, pp. 131-141. | JFM 51.0567.01

[17] C. Itzykson and J.-B. Zuber, Quantum Field Theory, McGraw Hill, New York, 1980. | MR 585517

[18] H. Kneser, Der Simplexinhalt in der nichteuklidischen Geometrie, Deutsche Math., vol. 1, 1936, pp. 337-340. | Zbl 0014.36203

[19] L. Lewin, Polylogarithms and Associated Functions, Elsevier, New York, 1981. | MR 618278 | Zbl 0465.33001

[20] E.B. Manoukian, Renormalization, Academic Press, New York, 1983. | MR 749231 | Zbl 0542.60094

[21] D.B. Melrose, Reduction of Feynman diagrams, Nuovo Cimento, vol. 40 A, 1965, pp. 181-213. | MR 192807 | Zbl 0137.45701

[22] J. Milnor, Hyperbolic geometry: The first 150 years, Bull. Amer. Math. Soc. (N. S.), vol. 6, 1982, pp. 9-24. | MR 634431 | Zbl 0486.01006

[23] N. Nakanishi, Graph Theory and Feynman Integrals, Gordon and Breach, New York, 1971. | Zbl 0212.29203

[24] W.L. Van Neerven and J.A.M. Vermaseren, Large loop integrals, Phys. Lett., vol. 137 B, 1984, pp. 241-244.

[25] G.J. Van Oldenborgh and J.A.M. Vermaseren, New algorithms for one-loop integrals, Z. Phys. C, vol. 46, 1990, pp. 425-437. | MR 1050544

[26] N. Ortner, Methods of construction of fundamental solutions of decomposable linear differential operators, in Boundary element methods IX. vol. 1, ed. by C. A. BREBBIA, W. L. WENDLAND and G. KUHN, CMP, Springer, Berlin, 1987, pp. 79-97. | MR 965314

[27] N. Ortner and P. Wagner, Feynman integral formulae and fundamental solutions of decomposable evolution operators, Proc. Steklov Inst. (Vol. 203, in honour of V. S. VLADIMIROV's 70th birthday) (to appear). | Zbl 0909.35031

[28] E. Peschl, Winkelrelationen am Simplex und die Eulersche Charakteristik, Bayer. Akad. Wiss. Math.-nat. Kl., S.-B., 1955, 1956, pp. 319-345. | MR 79775 | Zbl 0075.15501

[29] B. Petersson, Reduction of one-loop Feynman diagrams with n vertices in m-dimensional Lorentz space, J. Math. Phys., vol. 6, 1965, pp. 1955-1959. | MR 184593

[30] H. Poincaré, Sur la généralisation d'un théorème élémentaire de géométrie, C. R. Acad. Sci. Paris, (1), vol. 140, 1905, pp. 113-117. | JFM 36.0601.02

[31] L. Schläfli, Theorie der vielfachen Kontinuität, in Gesammelte Mathematische Abhandlungen, Bd. I, Birkhauser, Basel, 1950, pp. 167-389.

[32] L. Schwartz, Théorie des distributions, Nouv. éd., Hermann, Paris, 1966. | MR 209834

[33] L. Schwartz, Méthodes mathématiques pour les sciences physiques, 2e éd., Hermann, Paris, 1965. | MR 143360

[34] A.C.-T. Wu, On the analytic properties of the 4-point function in perturbation theory, Mat. Fys. Dan. Vid. Selsk., vol. 33, No. 3, 1961, pp. 1-88. | MR 145881