Geodesic
Note on the construction of the Bogolyubov scattering operator in the $({:}\varphi^4{:})_2$ theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 11 (1972) no. 3, pp. 331-336 
W. F. Wrezinski. Note on the construction of the Bogolyubov scattering operator in the $({:}\varphi^4{:})_2$ theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 11 (1972) no. 3, pp. 331-336. http://geodesic.mathdoc.fr/item/TMF_1972_11_3_a5/
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     title = {Note on the construction of the {Bogolyubov} scattering operator in the $({:}\varphi^4{:})_2$ theory},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The Bogolyubov scattering operator $S(g)$ is constructed for the ${:}\varphi^4{:}_2$ theory in the special case when the space-time cutoff has a product structure that consists of two smooth functions: one corresponding to a time cutoff and the other to a space cutoff. Unitarity and causality are verified for this operator. The generalization of these results to a large class of cutoffs is discussed.

[1] J. Glimm, A. Jaffe, Les Houches Lectures 1970, Gordon, N.-Y., 1971 (to appear) | Zbl

[2] N. N. Bogolyubov, D. V. Shirkov, Vvedenie v teoriyu kvantovannykh polei, Fizmatgiz, 1956 | MR

[3] B. Simon, R. Hoegh-Krohn, J. Funct. Analysis (to appear)

[4] Chastnoe soobschenie K. Kheppu

[5] K. Yosida, Functional Analysis, Springer Verlag, 1965 ; K. Iosida, Funktsionalnyi analiz, «Mir», 1968 | MR | MR

[6] V. Faris, J. Funct. Analysis, 1 (1964), 93 | DOI | MR

[7] E. Nelson, J. Math. Phys., 5 (1964), 332 | DOI | MR | Zbl