This paper studies the model of the quantum electrodynamics (QED) of a single
nonrelativistic electron due to W. Pauli and M. Fierz and studied further by P.
Blanchard. This model exhibits infrared divergence in a very simple context.
The infrared divergence is associated with the inequivalence of the Hilbert
spaces associated with the free Hamiltonian and with the complete Hamiltonian.
Infrared divergences that are visible in the perturbative description disappear
in the space of the clothed electrons. In this model when the Hamiltonian is
expressed in terms of the ``physical'' fields that create the electron together
with its cloud of soft photons the variational principle suggested earlier can
be applied. At finite time the Heisenberg field of the model acts in the space
of the perturbative electron together with a finite number of perturbative
photons, while the ``physical'' field can be chosen to act in the space of the
exact (``physical'') electron eigenstates together with a finite number of
physical photons. The space of the physical (or clothed) electron states can be
chosen to be a Fock space.Comment: 11 pages, no figures, to appear in Found. Phys., Vol. 30, No.3 (March
2000) (first issue in honor of Kurt Haller
