Geodesic
System of equations for the vertex functions of the $T$-exponential function
Teoretičeskaâ i matematičeskaâ fizika, Tome 14 (1973) no. 3, pp. 342-356

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An operator-valued functional of the “cutoff parameters” is constructed; after a certain formal passage to the limit this goes over into the renormaltzed perturbation series for the $S$-matrix of a scalar field with the interactions$\lambda\,{:}\varphi^3{:}$, $\lambda\,{:}\varphi^4{:}$. The characteristic equation obtained for it enables one to construct a system of equations that do not contain ultraviolet divergences for the vertex functions of the $\Sigma_n$ contributions from all strongly connected diagrams with $n$ external lines. 
@article{TMF_1973_14_3_a5,
     author = {V. A. Shcherbina},
     title = {System of equations for the vertex functions of the $T$-exponential function},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {342--356},
     publisher = {mathdoc},
     volume = {14},
     number = {3},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1973_14_3_a5/}
}
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V. A. Shcherbina. System of equations for the vertex functions of the $T$-exponential function. Teoretičeskaâ i matematičeskaâ fizika, Tome 14 (1973) no. 3, pp. 342-356. http://geodesic.mathdoc.fr/item/TMF_1973_14_3_a5/