Pair Production Problem and Canonical Quantization of Nonlinear Scalar
Field in Terms of World Lines
Yuri A. Rylov
Institute for Problems in Mechanics, Russian Academy of Science
101 Vernadskii Ave., Moscow, 117526, Russia.
Updated August 22, 2001
Abstract
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).
English version of the paper and figure
in Postscript.
Russian version of the paper and figure
in Postscript.