Asao Arai
Non-relativistic Limit of a Dirac-Maxwell Operator
in Relativistic Quantum Electrodynamics
(66K, LaTeX 2.09)
ABSTRACT. The non-relativistic (scaling) limit of
a particle-field Hamiltonian $H$, called
a Dirac-Maxwell operator,
in relativistic quantum electrodynamics is considered.
It is proven that the non-relativistic limit
of $H$ yields
a self-adjoint extension of
the Pauli-Fierz Hamiltonian with spin $1/2$
in non-relativistic quantum electrodynamics.
This is done by establishing in an abstract framework
a general limit theorem
on a family of self-adjoint
operators partially
formed out of strongly anticommuting self-adjoint operators
and then by applying
it to $H$.