no. 1
On the evaluation of one-loop Feynman amplitudes in euclidean quantum field theory
Annales de l'I.H.P. Physique théorique, Tome 63 (1995) no. 1, pp. 81-110. 
@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},
     pages = {81--110},
     publisher = {Gauthier-Villars},
     volume = {63},
     number = {1},
     year = {1995},
     mrnumber = {1354440},
     zbl = {0835.46042},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1995__63_1_81_0/}
}
TY  - JOUR
AU  - Ortner, N.
AU  - Wagner, P.
TI  - On the evaluation of one-loop Feynman amplitudes in euclidean quantum field theory
JO  - Annales de l'I.H.P. Physique théorique
PY  - 1995
SP  - 81
EP  - 110
VL  - 63
IS  - 1
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPA_1995__63_1_81_0/
LA  - en
ID  - AIHPA_1995__63_1_81_0
ER  - 
%0 Journal Article
%A Ortner, N.
%A Wagner, P.
%T On the evaluation of one-loop Feynman amplitudes in euclidean quantum field theory
%J Annales de l'I.H.P. Physique théorique
%D 1995
%P 81-110
%V 63
%N 1
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPA_1995__63_1_81_0/
%G en
%F 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) no. 1, pp. 81-110. http://www.numdam.org/item/AIHPA_1995__63_1_81_0/

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

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

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

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

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

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

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

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

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

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

[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 | Zbl

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

[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

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

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

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

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

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

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

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

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

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

[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

[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

[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

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

[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

[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

[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

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

[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