One Particle Binding of Many-Particle Semi-Relativistic Pauli-Fierz Model

It is shown that at least one particle is bound in the $N$-particle semi-relativistic Pauli-Fierz model with negative potential $V(\bx)$. It is assumed that the particles have no spin and obey the Bose or Boltzmann statistics, and the one particle Hamiltonian $\sqrt{-\Delta+M^2}-M+ V(\bx)$ has a ground state with negative energy $-e_0<0$, where $M>0$ denotes the mass of the particle. We show that the ground state energy of the total system $E^V(N)$ is less than $E^0(N)-e_0$.