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TMF, 1982, Volume 53, Number 3, Pages 358–373 (Mi tmf2623)  

This article is cited in 3 scientific papers (total in 3 papers)

Explicitly integrable models of quantum field theory with exponential interaction in two-dimensional space

A. N. Leznov, I. A. Fedoseev


Abstract: Explicit expressions are obtained for the Heisenberg operators of the two-dimensional models of quantum field theory described by the system of equations $\square u_\alpha=g\exp(ku)_\alpha$ as functionals of asymptotic fields $\varphi_\alpha^\mathrm{in}$ satisfying the equations $\square\varphi_\alpha^\mathrm{in}=0$ and appropriate commutation relations. It is shown that in the presence of a finite-dimensional internal symmetry group, when $k$ is the Caftan matrix of a semisimple Lie group, the perturbation series for the operators $\exp(-u_\alpha)$ degenerate into polynomials in the coupling constant $g$, the degrees of the polynomials being related to the structure of the fundamental representations of the corresponding group.

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English version:
Theoretical and Mathematical Physics, 1982, 53:3, 1175–1185

Bibliographic databases:

Received: 09.03.1982

Citation: A. N. Leznov, I. A. Fedoseev, “Explicitly integrable models of quantum field theory with exponential interaction in two-dimensional space”, TMF, 53:3 (1982), 358–373; Theoret. and Math. Phys., 53:3 (1982), 1175–1185

Citation in format AMSBIB
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\by A.~N.~Leznov, I.~A.~Fedoseev
\paper Explicitly integrable models of quantum field theory with exponential interaction in two-dimensional space
\jour TMF
\yr 1982
\vol 53
\issue 3
\pages 358--373
\mathnet{http://mi.mathnet.ru/tmf2623}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=693608}
\transl
\jour Theoret. and Math. Phys.
\yr 1982
\vol 53
\issue 3
\pages 1175--1185
\crossref{https://doi.org/10.1007/BF01027797}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1982QZ66700004}


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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. A. N. Leznov, M. A. Mukhtarov, “Internal symmetry algebra of exactly integrable dynamical systems in the quantum domain”, Theoret. and Math. Phys., 71:1 (1987), 370–375  mathnet  crossref  mathscinet  isi
    2. A. N. Leznov, “Integrable two-dimensional ultra-Toda mappings and chains”, Theoret. and Math. Phys., 117:1 (1998), 1194–1207  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. A. N. Leznov, “Graded Lie algebras, representation theory, integrable mappings, and integrable systems”, Theoret. and Math. Phys., 122:2 (2000), 211–228  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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