  A new quantization scheme (WL-scheme), using world lines as objects of
quantization, is proposed. Applying to nonlinear scalar field, the WL -scheme
is investigated and compared with the conventional PA-scheme of quantization.
In the PA-scheme objects of quantization are particles and antiparticles, which
are fragments of the total physical object -- world line (WL). Applying to the
nonlinear field, the PA-scheme of quantization leads to such difficulties as
nonstationary vacuum, obligatory use of perturbation theory technique, normal
ordering and cut-off in the scattering problem. These difficulties are
corollaries of inconsistency of PA-scheme. The WL-scheme is free of these
difficulties. These difficulties are connected with the reconstruction problem
of the total world lines from their fragments (particles and antiparticles). In
the case, when these fragments interact between themselves, such a
reconstruction is very complicated problem. The new WL-scheme of quantization
is free of all these problems, because it does not cut the total world line
into fragments (particles and antiparticles). Formally appearance of fragments
in the conventional quantization PA-scheme is a corollary of identification of
the energy with the Hamiltonian. In fact such an identification is not
necessary. It leads only to difficulties. The new WL-scheme of quantization
does not use this identification and enables to go around all these problems.
The WL-scheme enables not to use additional (to nonrelativistic QM)
quantization rules, used in the relativistic QFT (normal ordering, perturbation
technique, renormalization).
