Geodesic
Scattering theory for a~class of two-particle operators of mathematical physics (the case of weak interaction)
Izvestiya. Mathematics , Tome 76 (2012) no. 6, pp. 1077-1109

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

We study the spectral properties of two-particle operators $A$ with weak interaction for spatial dimension $d\geqslant3$. We show that such an operator is unitarily equivalent to the two-particle operator $A_0$ obtained from $A$ by omitting the interaction terms. This is done using a special diagrammatic technique developed in this paper.
Keywords: two-particle operator, wave operators, Cook's method, stationary phase method, diagrams. 
@article{IM2_2012_76_6_a1,
     author = {\`E. R. Akchurin and R. A. Minlos},
     title = {Scattering theory for a~class of two-particle operators of mathematical physics (the case of weak interaction)},
     journal = {Izvestiya. Mathematics },
     pages = {1077--1109},
     publisher = {mathdoc},
     volume = {76},
     number = {6},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2012_76_6_a1/}
}
TY  - JOUR
AU  - È. R. Akchurin
AU  - R. A. Minlos
TI  - Scattering theory for a~class of two-particle operators of mathematical physics (the case of weak interaction)
JO  - Izvestiya. Mathematics 
PY  - 2012
SP  - 1077
EP  - 1109
VL  - 76
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2012_76_6_a1/
LA  - en
ID  - IM2_2012_76_6_a1
ER  - 
%0 Journal Article
%A È. R. Akchurin
%A R. A. Minlos
%T Scattering theory for a~class of two-particle operators of mathematical physics (the case of weak interaction)
%J Izvestiya. Mathematics 
%D 2012
%P 1077-1109
%V 76
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2012_76_6_a1/
%G en
%F IM2_2012_76_6_a1
È. R. Akchurin; R. A. Minlos. Scattering theory for a~class of two-particle operators of mathematical physics (the case of weak interaction). Izvestiya. Mathematics , Tome 76 (2012) no. 6, pp. 1077-1109. http://geodesic.mathdoc.fr/item/IM2_2012_76_6_a1/