  Ground states of the so called Yukawa model is considered. The Yukawa model
describes a Dirac field interacting with a Klein-Gordon field. By introducing
both ultraviolet cutoffs and spatial cutoffs, the total Hamiltonian is defined
as a self-adjoint operator on a boson-fermion Fock space. It is shown that the
total Hamiltonian has a positive spectral gap for all values of coupling
constants. In particular the existence of ground states is proven.
