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

Ground States of the Yukawa models with Cutoffs