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 TMF, 1986, Volume 68, Number 3, Pages 338–349 (Mi tmf5187)

Heisenberg fields in the neighborhood of a classical solution

V. B. Tverskoi

Abstract: For the example of nonlinear models of a scalar field in two-dimensional space-time a study is made of a method of quantization in the neighborhood of a classical solution based on direct solution by perturbation theory of the Cauchy problem for the Heisenberg field equations. It is shown that, as in the classical Bogolyubov–Krylov method, zero modes and associated secular terms arise because of the perturbation-theory expansion of the Bogolyubov operator argument of the classical component. The Lehmann–Symanzik–Zimmermann procedure is used to make a complete investigation of the asymptotic states of the field in the soliton sector in the lowest orders of perturbation theory.

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English version:
Theoretical and Mathematical Physics, 1986, 68:3, 866–873

Bibliographic databases:

Citation: V. B. Tverskoi, “Heisenberg fields in the neighborhood of a classical solution”, TMF, 68:3 (1986), 338–349; Theoret. and Math. Phys., 68:3 (1986), 866–873

Citation in format AMSBIB
\Bibitem{Tve86} \by V.~B.~Tverskoi \paper Heisenberg fields in the neighborhood of a~classical solution \jour TMF \yr 1986 \vol 68 \issue 3 \pages 338--349 \mathnet{http://mi.mathnet.ru/tmf5187} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=871058} \transl \jour Theoret. and Math. Phys. \yr 1986 \vol 68 \issue 3 \pages 866--873 \crossref{https://doi.org/10.1007/BF01019386} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1986G881200002} 

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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. K. A. Sveshnikov, “Quantium dynamics of an extended object in Bogolyubov's group variables”, Theoret. and Math. Phys., 74:3 (1988), 251–264
2. K. A. Sveshnikov, “Aspects of perturbation theory in the neighborhood of a classical particle-like solution”, Theoret. and Math. Phys., 76:3 (1988), 911–919
3. K. A. Sveshnikov, P. K. Silaev, “Connection between discontinuous step-like and smooth kink-type classical solutions in quantum field theory”, Theoret. and Math. Phys., 108:2 (1996), 1019–1045
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