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 Mat. Sb., 1991, Volume 182, Number 2, Pages 236–282 (Mi msb1294)

Quantum scattering in gauge fields of adiabatic representations

Yu. A. Kuperin, Yu. B. Melnikov

Abstract: A geometric approach to the method of adiabatic representations is developed for a class of relativistic Hamiltonians. The theory is used to analyze the associated dynamical equations with effective nonabelian interactions that can be regarded as gauge fields, induced by dimensional reduction of the initial problem in a special representation. It is shown that the approach can be used to study $2\to(2,3)$ quantum scattering processes in a three-body system, and a one-to-one relation between the complete and the effective $S$-matrices is derived. Asymptotic expressions are found for the solutions of the effective dynamical equation and for the gauge fields in the adiabatic representations. The method is illustrated for systems admitting adiabatic representations with a one-dimensional base; in several cases the field operator is proved to be Hilbert–Schmidt.

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English version:
Mathematics of the USSR-Sbornik, 1992, 72:1, 221–265

Bibliographic databases:

UDC: 530.145
MSC: 81Q10, 81U20

Citation: Yu. A. Kuperin, Yu. B. Melnikov, “Quantum scattering in gauge fields of adiabatic representations”, Mat. Sb., 182:2 (1991), 236–282; Math. USSR-Sb., 72:1 (1992), 221–265

Citation in format AMSBIB
\Bibitem{KupMel91} \by Yu.~A.~Kuperin, Yu.~B.~Melnikov \paper Quantum scattering in gauge fields of adiabatic representations \jour Mat. Sb. \yr 1991 \vol 182 \issue 2 \pages 236--282 \mathnet{http://mi.mathnet.ru/msb1294} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1103274} \zmath{https://zbmath.org/?q=an:0776.47044|0744.47053} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1992SbMat..72..221K} \transl \jour Math. USSR-Sb. \yr 1992 \vol 72 \issue 1 \pages 221--265 \crossref{https://doi.org/10.1070/SM1992v072n01ABEH001412} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1992JF72300013} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. Yu.A. Kuperin, B.S. Pavlov, G.E. Rudin, S.I. Vinitsky, “Spectral geometry: two exactly solvable models”, Physics Letters A, 194:1-2 (1994), 59
2. Suzko A., Velicheva E., “Exactly Soluble Two-Dimensional Models in the Adiabatic Representation”, Phys. Atom. Nuclei, 59:6 (1996), 1087–1103
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