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Izvestiya: Mathematics, 2012, Volume 76, Issue 6, Pages 1077–1109
DOI: https://doi.org/10.1070/IM2012v076n06ABEH002615 (Mi im6938) 		 
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
English version PDF (762 kB) Citations (2) Russian version article
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DOI: https://doi.org/10.1070/IM2012v076n06ABEH002615
Abstract: 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.
Received: 04.02.2011
Revised: 23.03.2012
Bibliographic databases:
Document Type: Article
UDC: 517.98
MSC: 47A40, 35P25, 81U05
Language: English
Original paper language: Russian
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. Math., 76:6 (2012), 1077–1109
Citation in format AMSBIB
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\by \`E.~R.~Akchurin, R.~A.~Minlos
\paper Scattering theory for a~class of two-particle operators of mathematical physics (the case of weak interaction)
\jour Izv. Math.
\yr 2012
\vol 76
\issue 6
\pages 1077--1109
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  • https://doi.org/10.1070/IM2012v076n06ABEH002615
  • https://www.mathnet.ru/eng/im/v76/i6/p5
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
     
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