Quantization of solitons

We hope that we have succeeded in convincing the reader that this one-dimensional nonlinear model of field theory has a number of attractive properties. Let us list some of them. 1. The Lagrangian of the theory contains only one field, but a complete spectrum of particles is manifested. In the weak interaction approximation the solitons are heavy particles and they interact strongly. 2. The solitons have a quantum number which has a topological nature, and this can be interpreted as a charge. Solitons with the same charge repel each other, while solitons with different charge attract oacl other. 3. In the weak interaction approximation a prescription exists for calculating in perturbation theory. The quantum corrections are small for small coupling constants, and the quasiclassical treatment determines the entire nonanalytic contribution to the physical quantities. The contents of this paper have been frequently discussed and corrected in collaboration with our colleagues I. Ya. Aref'evaya, P. P. Kulish, V. N. Popov, and L. A. Takhtadzhyan. We are very grateful to them. The paper was partly reworked after one of the authors (L. D. Faddeev) had been to the United States, where the paper was discussed with R. Dashen, R. Jackiw, S. Coleman, A. Neveu, and B. Hasslacher.