Enhanced binding for N -particle system interacting with a scalar bose field I

An enhanced binding of an N -particle system interacting through a scalar bose field is investigated, where N ≥ 2. It is not assumed that this system has a ground state for a zero coupling. It is shown, however, that there exists a ground state for a sufficiently large values of coupling constants. When the coupling constant is sufficiently large, N particles are bound to each other by the scalar bose field, and are trapped by external potentials. Basic ideas of the proofs in this paper are applications of a weak coupling limit and a modified HVZ theorem.