Connection between discontinuous step-like and smooth kink-type classical solutions in quantum field theory

Non-perturbative procedure for subtraction of singularities, caused by discontinuous step-like solutions in nonlinear QFT is suggested. We discuss in details the procedure of Lorentz-covariant quantization for topological kinks in (1+1) nonlinear field models. It had been shown that the “quantum copies” of classical kink appears as the result of this procedure. These copies have the same topological charge, but negligibly small size. Moreover, they have negligibly small mass, due to subtraction procedure, that eliminate divergent terms that are proportional to squared delta-function. We give the detailed discussion of these problems for various (1+1) nonlinear models with classical kinks.