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Izv. RAN. Ser. Mat., 2012, Volume 76, Issue 6, Pages 5–38 (Mi izv6938)  

This article is cited in 2 scientific papers (total in 2 papers)

Scattering theory for a class of two-particle operators of mathematical physics (the case of weak interaction)

È. R. Akchurina, R. A. Minlosab

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow

Abstract: We study the spectral properties of two-particle operators $A$ with weak interaction for spatial dimension $d\ge3$. 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.

DOI: https://doi.org/10.4213/im6938

Full text: PDF file (1009 kB)
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English version:
Izvestiya: Mathematics, 2012, 76:6, 1077–1109

Bibliographic databases:

UDC: 517.98
MSC: 47A40, 35P25, 81U05
Received: 04.02.2011
Revised: 23.03.2012

Citation: È. R. Akchurin, R. A. Minlos, “Scattering theory for a class of two-particle operators of mathematical physics (the case of weak interaction)”, Izv. RAN. Ser. Mat., 76:6 (2012), 5–38; Izv. Math., 76:6 (2012), 1077–1109

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. R. Akchurin, R. A. Minlos, “On a method in scattering theory”, Trans. Moscow Math. Soc., 72 (2011), 143–156  mathnet  crossref  zmath  elib
    2. Yu. Kh. Èshkabilov, “Spectrum of a model three-particle Schrödinger operator”, Theoret. and Math. Phys., 186:2 (2016), 268–279  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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