  HVZ type theorem for semi-relativistic Pauli-Fierz Hamiltonian,
$$\HHH=\sqrt{(p\otimes \one -A)^2+M^2}+V\otimes \one +\one\otimes \hf,\quad
M\geq 0,$$ in quantum electrodynamics is studied. Here $H$ is a self-adjoint
operator in Hilbert space $\LR\otimes \fff\cong \int^\oplus_{\RR^d}\fff {\rm
d}x$, and $A=\int^\oplus_{\RR^d} A(x) {\rm d}x$ a quantized radiation field and
$\hf$ the free field Hamiltonian defined by the second quantization of a
dispersion relation $\omega:\RR^d\to \RR$. It is emphasized that massless case,
$M=0$, is included. Let $E=\inf \sigma (\HHH)$ be the bottom of the spectrum of
$\HHH$. Suppose that the infimum of $\omega$ is $m>0$. Then it is shown that
$\sigma_{\rm ess}(\HHH)=[E+m, \infty)$. In particular the existence of the
ground state of $\HHH$ can be proven.
