Singular structure of Feynman diagrams
Teoretičeskaâ i matematičeskaâ fizika, Tome 41 (1979) no. 3, pp. 330-335
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It is shown that the singularities of any Feynman diagram $G_k(x_1,\dots,x_k)$ in the coordinate space lie on an algebraic surface. For diagrams with one internal vertex, the equation of this surface has the form $\det S=0$, where $S$ is the matrix composed of the elements $s_{jj'}=(x_j-x_j')^2$. In the general case, the equation of the singularity surface is obtained as the necessary and sufficient condition for the existence of a nontrivial solution to a homogeneous algebraic system of equations, this system being derived by means of the
concept of the wave front of a generalized function. It is shown how this system of equations can be obtained from the ordinary $\alpha$ representation for Feynmml diagrams.
@article{TMF_1979_41_3_a3,
author = {V. A. Smirnov},
title = {Singular structure of {Feynman} diagrams},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {330--335},
publisher = {mathdoc},
volume = {41},
number = {3},
year = {1979},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1979_41_3_a3/}
}
V. A. Smirnov. Singular structure of Feynman diagrams. Teoretičeskaâ i matematičeskaâ fizika, Tome 41 (1979) no. 3, pp. 330-335. http://geodesic.mathdoc.fr/item/TMF_1979_41_3_a3/