Geodesic
Two-dimensional model of the interaction of a nonrelativistic particle with scalar mesons in the strong-coupling limit
Teoretičeskaâ i matematičeskaâ fizika, Tome 76 (1988) no. 2, pp. 231-241 
A. A. Torotadze; A. V. Shurgaya. Two-dimensional model of the interaction of a nonrelativistic particle with scalar mesons in the strong-coupling limit. Teoretičeskaâ i matematičeskaâ fizika, Tome 76 (1988) no. 2, pp. 231-241. http://geodesic.mathdoc.fr/item/TMF_1988_76_2_a6/
@article{TMF_1988_76_2_a6,
     author = {A. A. Torotadze and A. V. Shurgaya},
     title = {Two-dimensional model of the interaction of a~nonrelativistic particle with scalar mesons in the strong-coupling limit},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {231--241},
     year = {1988},
     volume = {76},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1988_76_2_a6/}
}
TY  - JOUR
AU  - A. A. Torotadze
AU  - A. V. Shurgaya
TI  - Two-dimensional model of the interaction of a nonrelativistic particle with scalar mesons in the strong-coupling limit
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1988
SP  - 231
EP  - 241
VL  - 76
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1988_76_2_a6/
LA  - ru
ID  - TMF_1988_76_2_a6
ER  - 
%0 Journal Article
%A A. A. Torotadze
%A A. V. Shurgaya
%T Two-dimensional model of the interaction of a nonrelativistic particle with scalar mesons in the strong-coupling limit
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1988
%P 231-241
%V 76
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1988_76_2_a6/
%G ru
%F TMF_1988_76_2_a6

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

Bogolyubov transformations are introduced in the nonrelativistic model of the interaction of a particle with scalar mesons. A translationally invariant perturbation theory in reciprocal powers of the coupling constant is constructed in the framework of the generalized Hamiltonian formalism developed by Dirac. The transmission and reflection coefficients are obtained. The $S$ matrix is expressed in a holomorphic representation and the matrix elements are calculated.

[1] Bogolyubov N. N., Izbrannye trudy v trekh tomakh, Naukova dumka, Kiev, 1970, S. 499–519. | MR

[2] Solodovnikova E. P., Tavkhelidze A. N., Khrustalev O. A., TMF, 11:3 (1972), 317–330

[3] Razumov A. V., Khrustalev O. A., TMF, 29:3 (1976), 300–308 | MR

[4] Solodovnikova E. P., Tavkhelidze A. N., Khrustalev O. A., TMF, 10:2 (1972), 162–181 ; Архипов А. А., Тюрин Н. Е., ТМФ, 17:1 (1973), 57–66 ; Тимофеевская О. Д., Тюрин Н. Е., Шургая А. В., ТМФ, 17:1 (1973), 79–89

[5] Christ N. H., Lee T. D., Phys. Rev., D12:6 (1975), 1606–1627 | MR

[6] Gervats G. L., Sakita B., Phys. Rev., D11:10 (1975), 2943–2945 ; Gervais J. L., Jeviski A., Sakita B., Phys. Rev., D12:4 (1975), 1038–1051 ; Tomboulis E., Woo G., Ann. Phys., 98:4 (1976), 1–13 | DOI

[7] Dirak P., Lektsii po kvantovoi mekhanike, Mir, M., 1968

[8] Shurgaya A. V., TMF, 45:1 (1980), 46–53 | MR

[9] Torotadze A. A., Shurgaya A. V., Metod kollektivnykh peremennykh i obobschennyi gamiltonov formalizm v zadache dvukh tel, Preprint OTF 82-192, IFVE, Serpukhov, 1982

[10] Razumov A. V., Taranov A. Yu., TMF, 35:3 (1978), 312–321 | MR

[11] Faddeev L. D., TMF, 1:1 (1969), 3–18 | MR | Zbl

[12] Berezin F. A., Metod vtorichnogo kvantovaniya, Nauka, M., 1965 | MR

[13] Faddeev L. D., Corepin V. E., Phys. Rep., 42C:1 (1978) | MR