On the Absence of Bound States in the λϕ24 Quantum Field Model Without Symmetry Breaking

Abstract

We study a λϕ24 model with a unique vacuum, invariant under the symmetry ϕ → −ϕ, and we assume that certain connected 4n-point Euclidean Green's functions are negative. Then the mass operator, M = (H2 – P2)1/2, restricted to the space of states that are even under ϕ → −ϕ, has no spectrum in the interval (0, 2m). In particular, two particle bound states do not occur in the single phase region (i.e. λ < λcritical).