Hamiltonian models of interacting fermion fields in Quantum Field Theory

We consider hamiltonian models representing an arbitrary number of spin $1/2$ fermion quantum fields interacting through arbitrary processes of creation or annihilation of particles. The fields may be massive or massless. The interaction form factors are supposed to satisfy some regularity conditions in both position and momentum space. Without any restriction on the strength of the interaction, we prove that the Hamiltonian identifies to a self-adjoint operator on a tensor product of anti-symmetric Fock spaces and we establish the existence of a ground state. Our results rely on new interpolated $N_τ$ estimates. They apply to models arising from the Fermi theory of weak interactions, with ultraviolet and spatial cut-offs.

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