On the number of eigenvalues of a model operator in fermionic Fock space (original) (raw)

We consider a model describing a truncated operator H (truncated with respect to the number of particles) acting in the direct sum of zero-, one-, and two-particle subspaces of a fermionic Fock space Fa(L 2 (T 3 )) over L 2 (T 3 ). We admit a general form for the "kinetic" part of the hamiltonian H, which contains a parameter γ to distinguish the two identical particles from the third one. In this note: (i) We find a critical value γ * for the parameter γ that allows or forbids the Efimov effect (infinite number of bound states if the associated generalized Friedrichs model has a threshold resonance) and we prove that only for γ < γ * the Efimov effect is absent, while this effect exists for any γ > γ * .