  A system of a Dirac particle interacting with the radiation field is
considered. The Hamiltonian of the system is defined by $H =
\alpha\cdot(\hat\mathbf{p}-q\mathbf{A}(\hat\mathbf{x}))+m\beta + H_f$ where
$q\in\mathbb{R}$ is a coupling constant, $\mathbf{A}(\hat\mathbf{x})$ denotes
the quantized vector potential and $H_f$ denotes the free photon Hamiltonian.
Since the total momentum is conserved, $H$ is decomposed with respect to the
total momentum with fiber Hamiltonian $H(\mathbf{p}),
(\mathbf{p}\in\mathbb{R}^3)$. Since the self-adjoint operator $H(\mathbf{p})$
is bounded from below, one can define the lowest energy
$E(\mathbf{p},m):=\inf\sigma(H(\mathbf{p}))$. We prove that $E(\mathbf{p},m)$
is an eigenvalue of $H(\mathbf{p})$ under the following conditions: (i)
infrared regularization and (ii) $E(\mathbf{p},m)<E(\mathbf{p},0)$. We also
discuss the polarization vectors and the angular momenta.
