Geodesic
Functional integral for the scattering amplitude in the presence of a long-range interaction
Teoretičeskaâ i matematičeskaâ fizika, Tome 41 (1979) no. 1, pp. 12-25 
A. N. Vasil'ev; A. V. Kuzmenko. Functional integral for the scattering amplitude in the presence of a long-range interaction. Teoretičeskaâ i matematičeskaâ fizika, Tome 41 (1979) no. 1, pp. 12-25. http://geodesic.mathdoc.fr/item/TMF_1979_41_1_a2/
@article{TMF_1979_41_1_a2,
     author = {A. N. Vasil'ev and A. V. Kuzmenko},
     title = {Functional integral for the scattering amplitude in the presence of a~long-range interaction},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {12--25},
     year = {1979},
     volume = {41},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1979_41_1_a2/}
}
TY  - JOUR
AU  - A. N. Vasil'ev
AU  - A. V. Kuzmenko
TI  - Functional integral for the scattering amplitude in the presence of a long-range interaction
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1979
SP  - 12
EP  - 25
VL  - 41
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1979_41_1_a2/
LA  - ru
ID  - TMF_1979_41_1_a2
ER  - 
%0 Journal Article
%A A. N. Vasil'ev
%A A. V. Kuzmenko
%T Functional integral for the scattering amplitude in the presence of a long-range interaction
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1979
%P 12-25
%V 41
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1979_41_1_a2/
%G ru
%F TMF_1979_41_1_a2

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

A generalization is obtained of the functional integral for the scattering amplitude (and also for the stationary wave function of the scattering problem) in the case of “moderate” long-range interactions, i.e., in the case of potentials $\mathfrak{b}(r)$ having the behavior $zr^{-\lambda}$, $1/2<\lambda\leqslant1$, for large $r$. The quasiclassieal expansion of the scattering amplitude is considered.

[1] W. B. Campbell, P. Finkler, C. E. Jones, M. N. Misheloff, Phys. Rev., D12 (1975), 2363

[2] A. N. Vasilev, A. V. Kuzmenko, TMF, 31 (1977), 313 | MR

[3] J. Dollard, J. Math. Phys., 5 (1964), 729 | DOI | MR

[4] R. Feynman, Rev. Mod. Phys., 20 (1948), 367 | DOI | MR

[5] R. Feynman, Phys. Rev., 84 (1951), 108 | DOI | MR | Zbl

[6] F. A. Berezin, TMF, 6 (1971), 194 | MR | Zbl

[7] M. Kats, Veroyatnost i smezhnye voprosy v fizike, «Mir», 1965 | Zbl

[8] A. N. Vasilev, Funktsionalnye metody v kvantovoi teorii polya i statistike, LGU, 1976

[9] L. D. Faddeev, V. N. Popov, Phys. Lett., 25B (1967), 29 | DOI

[10] A. V. Kuzmenko, TMF, 29 (1976), 52 | MR

[11] A. M. Veselova, TMF, 13 (1972), 368

[12] G. E. Shilov, Fan Dyk Tin, Integral, mera i proizvodnaya na lineinykh prostranstvakh, «Nauka», 1967 | MR