Geodesic
Singularities of Feynman diagrams in the coordinate space
Teoretičeskaâ i matematičeskaâ fizika, Tome 36 (1978) no. 2, pp. 183-192

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The wave front $WF(G_k)$ of an arbitrary Feynman diagram with $k$ external vertices is described. It is shown that $G_2(x_1,x_2)$ can have singularities only for $(x_1-x_2)^2=0$, and $G_3(x_1,x_2,x_3)$ only when $(x_j-x_{j'})^2=0$ for certain $j\ne j'$. It is shown that in the case of four or more external vertices the simplest diagrams have singularities not only on the light cones with respect to $x_j-x_{j'}$. 
@article{TMF_1978_36_2_a3,
     author = {V. A. Smirnov},
     title = {Singularities of {Feynman} diagrams in the coordinate space},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {183--192},
     publisher = {mathdoc},
     volume = {36},
     number = {2},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1978_36_2_a3/}
}
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V. A. Smirnov. Singularities of Feynman diagrams in the coordinate space. Teoretičeskaâ i matematičeskaâ fizika, Tome 36 (1978) no. 2, pp. 183-192. http://geodesic.mathdoc.fr/item/TMF_1978_36_2_a3/