Properties of the (: φ4 :)1 + 1 interaction Hamiltonian

Using a convergent expansion of the resolvent of the Hamiltonian H=H0+λ V, V=∫d x×(x):φ4:(x),g(x)∈C0∞,g(x)⩾0, we give a simple proof of (a) the self-adjointness of the Hamiltonian and (b) the volume independent lower bound of the vacuum energy per unit volume. Also, we obtain some coupling constant analyticity properties of the Hamiltonian, and the limit (H0+λν−z)−1→(H0−−z)−1, z ∈ρ(H0) in norm as |λ|→0 uniformly in {λ:|argλ|<π}.