 0635 Asao Arai
 Nonrelativistic Limit
of a Dirac Polaron
in Relativistic Quantum Electrodynamics
(21K, Latex2.09)
Feb 22, 06

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Abstract. A quantum system of a Dirac particle interacting with the quantum radiation field
is considered in the case where no external potentials exist. Then
the total momentum of the system is conserved and the total Hamiltonian
is unitarily equivalent to
the direct integral $\int_{{\bf R}^3}^\oplus\overline{H({\bf p})}d{\bf p}$
of a family of selfadjoint operators
$\overline{H({\bf p})}$ acting in the Hilbert space $\oplus^4{\cal F}_{\rm rad}$,
where ${\cal F}_{\rm rad}$ is the Hilbert space of
the quantum radiation field. The fibre operator $\overline{H({\bf p})}$ is
called the Hamiltonian of the Dirac polaron with total momentum ${\bf p}
\in {\bf R}^3$. The main result of this paper is concerned with
the nonrelativistic (scaling) limit of
$\overline{H({\bf p})}$. It is proven that the nonrelativistic limit
of $\overline{H({\bf p})}$ yields
a selfadjoint extension of
a Hamiltonian of a polaron with spin $1/2$
in nonrelativistic quantum electrodynamics.
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