  The spinless semi-relativistic Pauli-Fierz Hamiltonian $H$ in quantum
electrodynamics is considered. The self-adjointness and essential
self-adjointness of $H$ are shown. It is emphasized that it includes the
massless case. Furthermore, the self-adjointness and the essential
self-adjointness of the semi-relativistic Pauli-Fierz model with a fixed total
momentum is also proven.
