Geodesic
Method of extended $S$-matrix in quantum field theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 13 (1972) no. 1, pp. 3-40 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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B. V. Medvedev; V. P. Pavlov; M. K. Polivanov; A. D. Sukhanov. Method of extended $S$-matrix in quantum field theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 13 (1972) no. 1, pp. 3-40. http://geodesic.mathdoc.fr/item/TMF_1972_13_1_a0/

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