Geodesic
Triviality conditions for the $S$-matrix in the Haag–Ruelle scattering theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 15 (1973) no. 3, pp. 297-306 
V. D. Koshmanenko. Triviality conditions for the $S$-matrix in the Haag–Ruelle scattering theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 15 (1973) no. 3, pp. 297-306. http://geodesic.mathdoc.fr/item/TMF_1973_15_3_a0/
@article{TMF_1973_15_3_a0,
     author = {V. D. Koshmanenko},
     title = {Triviality conditions for the $S$-matrix in the {Haag{\textendash}Ruelle} scattering theory},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {297--306},
     year = {1973},
     volume = {15},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1973_15_3_a0/}
}
TY  - JOUR
AU  - V. D. Koshmanenko
TI  - Triviality conditions for the $S$-matrix in the Haag–Ruelle scattering theory
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1973
SP  - 297
EP  - 306
VL  - 15
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1973_15_3_a0/
LA  - ru
ID  - TMF_1973_15_3_a0
ER  - 
%0 Journal Article
%A V. D. Koshmanenko
%T Triviality conditions for the $S$-matrix in the Haag–Ruelle scattering theory
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1973
%P 297-306
%V 15
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1973_15_3_a0/
%G ru
%F TMF_1973_15_3_a0

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

In the framework of Hepp's formulation of Haag–Ruelle scattering theory, some conditions for the asymptotic fields to be identical are found. In particular, it is shown that the theory is trivial if an invertible operator relationship (whose boundedness is not assumed) exists between the states of the interpolating field and the states of one of the asymptotic fields.

[1] R. Striter, A. S. Vaitman, RST, spin i statistika i vse takoe, «Nauka», 1966

[2] R. Iost, Obschaya teoriya kvantovannykh polei, «Mir», 1967 | MR

[3] N. N. Bogolyubov, A. A. Logunov, I. T. Todorov, Osnovy aksiomaticheskogo podkhoda v kvantovoi teorii polya, «Nauka», 1969 | MR

[4] K. Hepp, Helv. Phys. Acta, 37 (1964), 639 | MR | Zbl

[5] K. Hepp, Commun. Math. Phys., 1 (1965), 111 | DOI | MR | Zbl

[6] K. Khepp, A. Epshtein, Analiticheskie svoistva amplitud rasseyaniya v lokalnoi kvantovoi teorii polya, Atomizdat, 1971

[7] R. Streater, J. Math. Phys., 8 (1967), 1685 | DOI | Zbl

[8] K. Fridrikhs, Vozmuschenie spektra operatorov v gilbertovom prostranstve, «Mir», 1969

[9] T. Kato, Perturbation theory for linear operators, Springer-Verlag, Berlin–Heidelberg–New York, 1966 | MR

[10] N. Danford, Dzh. T. Shvarts, Lineinye operatory. Obschaya teoriya, IL, 1962 | MR

[11] W. Garczynski, Bull. Acad. Polon. Sci., Ser. sci. math., astron. et phys., 14 (1966), 279

[12] W. Garczynski, V winter scool of Theoretical Physics in Karpacz, A, v. 1, Wroclaw, 1968, 123

[13] W. Garczynski, Nucl. Phys., B4 (1968), 689 | DOI