Anomalies of quantum currents in exactly solvable models

The quantum conserved currents of the sine-Gordon equation and the massive Thirring model are analyzed. The anomalous terms that arise in the Ward identities as a result of the renormalization lead only to multiplication by a constant of the laws of conservation of the sums of the corresponding powers of the momenta of the particles of the initial and the final state. Factorization of the $S$-matrix is preserved in the quantum theory in all perturbation orders.