Bogolyubov's $R$-operation for local interactions

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.