Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hamiltonian quantization of solitons in the $\phi^4_{1+1}$ quantum field
  theory. I. The semiclassical mass shift   We study of the interaction of a scalar quantum field $\phi $ with a fixed
(external) electromagnetic field $A^{ext}_\mu dx^\mu$ in two dimensional
space-time. The dynamics is determined by the action functional \[
S\,=\,\int\,\Bigl(\frac{1}{2}\partial_\mu\phi\partial^\mu\phi-
\frac{1}{2}\,g^2\bigl(\phi^2-\frac{m^2}{g^2}\bigr)^2
+\lambda\epsilon_{\mu\nu}\partial_\mu A^{ext}_\nu \phi\,\Bigr)\,dxdt\,. \] The
quartic interaction, a double well potential, supports the existence of
solitons in the classical theory. The existence of the corresponding quantum
theory can be proved by the methods of constructive quantum field theory. The
aim is to analyze the dynamics of the soliton in this quantized theory as $g\to
0 $, which corresponds to a nonrelativistic limit for the soliton, which has
mass which diverges as $g^{-2} $ in this limit. In this first paper attention
is focused on the case $\lambda=0$. We develop the analytical framework for
quantizing the theory, identify the appropriate degrees of freedom to describe
the soliton and the $g\to 0 $ limiting dynamics and provide an interpretation
and proof of the Dashen-Hasslacher-Neveu semiclassical mass correction formula.

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The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph