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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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},
     year = {1980},
     volume = {42},
     number = {2},
     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/

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