  An interaction system of a fermionic quantum field is considered. The state
space is defined by a tensor product space of a fermion Fock space and a
Hilbert space. It is assumed that the total Hamiltonian is a self-adjoint
operator on the state space and bounded from below. Then it is proven that a
subset of real numbers is the essential spectrum of the total Hamiltonian. It
is applied to the system of a Dirac field coupled to a Klein-Gordon field. Then
the HVZ theorem for the system is obtained.
