Geodesic
Projection-iteration method of~solution of~the equations of~quantum field theory and its connection with the theory of~renormalization. The equations of~quantum field theory and improperly posed problems of~mathematical physics
Teoretičeskaâ i matematičeskaâ fizika, Tome 42 (1980) no. 2, pp. 167-183

Voir la notice de l'article provenant de la source Math-Net.Ru

The equations for coefficient functions of the scattering matrix are considered in the Euclidean space-time of the dimension $d=4$. It is shown that they can be defined correctly in the pair of functional spaces of the translationally-inyariant functions. The problem of finding the solutions for such equations is stated improperly, therefore the iteration method of solution results in the arising of ultraviolet divergencies. A projection-iteration method of solution is constructed which leads to the renormalized perturbation theory series. Renormalized perturbation theory series is proved to be a quasisolution of the input equations. 
@article{TMF_1980_42_2_a1,
     author = {D. Ya. Petrina and A. L. Rebenko},
     title = {Projection-iteration method of~solution of~the equations of~quantum field theory and its connection with the theory of~renormalization. {The} equations of~quantum field theory and improperly posed problems of~mathematical physics},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {167--183},
     publisher = {mathdoc},
     volume = {42},
     number = {2},
     year = {1980},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1980_42_2_a1/}
}
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D. Ya. Petrina; A. L. Rebenko. Projection-iteration method of~solution of~the equations of~quantum field theory and its connection with the theory of~renormalization. The equations of~quantum field theory and improperly posed problems of~mathematical physics. Teoretičeskaâ i matematičeskaâ fizika, Tome 42 (1980) no. 2, pp. 167-183. http://geodesic.mathdoc.fr/item/TMF_1980_42_2_a1/