Abstract:
Parametric representations are constructed for the finite parts of Feynman amplitudes corresponding to the renormalized perturbation series for the $S$-matrix with a special regularization. These representations are obtained as limiting values for the Feynman amplitudes in spaces with indefinite metric, which enables one to verify unitarity and causality of the $S$-matrix in all perturbation orders.
Citation:
V. D. Gordevskii, O. V. Uvarov, I. Yu. Chudinovich, V. A. Shcherbina, “Bogolyubov's $R$-operation for local interactions”, TMF, 20:2 (1974), 147–159; Theoret. and Math. Phys., 20:2 (1974), 729–737