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 TMF, 1972, Volume 13, Number 1, Pages 3–40 (Mi tmf3233)

Method of extended $S$-matrix in quantum field theory

B. V. Medvedev, V. P. Pavlov, M. K. Polivanov, A. D. Sukhanov

Abstract: A general theory of extending the $S$-matrix off the mass shell is developed by introducing a dependence on functions that describe an arbitrary external classical object. A space-time description is introduced in terms of a classical functional argument of this kind; the description is needed to formulate causality, which is adopted in Bogolyubov's form. Systematic exploitation of this principle makes it possible to construct a detailed dynamical theory. Three well-known special cases of the classical object are considered: the interaction switching-on function, a classical addition to the quantized out-field, and a classical current source. The relationship between the two last methods of extension is established by the introduction of an $S$-matrix that is extended twice – with respect to the field and the current. This provides a basis for elucidating the relationship between the consequences of the Bogolyubov and the Lehmann–Symanzik–Zimmermann axiomatics.

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English version:
Theoretical and Mathematical Physics, 1972, 13:1, 939–964

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Revised: 28.04.1972

Citation: B. V. Medvedev, V. P. Pavlov, M. K. Polivanov, A. D. Sukhanov, “Method of extended $S$-matrix in quantum field theory”, TMF, 13:1 (1972), 3–40; Theoret. and Math. Phys., 13:1 (1972), 939–964

Citation in format AMSBIB
\Bibitem{MedPavPol72} \by B.~V.~Medvedev, V.~P.~Pavlov, M.~K.~Polivanov, A.~D.~Sukhanov \paper Method of extended $S$-matrix in quantum field theory \jour TMF \yr 1972 \vol 13 \issue 1 \pages 3--40 \mathnet{http://mi.mathnet.ru/tmf3233} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=475472} \transl \jour Theoret. and Math. Phys. \yr 1972 \vol 13 \issue 1 \pages 939--964 \crossref{https://doi.org/10.1007/BF01035414} 

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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. S. S. Ivanov, D. Ya. Petrina, A. L. Rebenko, “On equations for the coefficient functions of the $S$-matrix in quantum field theory”, Theoret. and Math. Phys., 19:1 (1974), 332–339
2. S. S. Ivanov, D. Ya. Petrina, A. L. Rebenko, “$S$ matrix in constructive quantum field theory”, Theoret. and Math. Phys., 23:2 (1975), 422–434
3. N. K. Dushutin, V. M. Mal'tsev, S. I. Sinegovskii, “Particle production in the extended $S$-matrix method”, Theoret. and Math. Phys., 24:1 (1975), 676–680
4. O. Yu. Shvedov, “Relativistically Covariant Quantum Field Theory of the Maslov Complex Germ”, Theoret. and Math. Phys., 144:3 (2005), 1296–1314
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