Uniqueness of the Vacuum Energy Density and van Hove Phenomenon in the Infinite-Volume Limit for Two-Dimensional Self-Coupled Bose Fields

For a class of model quantum field theories in two-dimensional space-time describing a neutral scalar boson field interacting in a region of length $l$, the vacuum energy density converges as $l\to \infty$. In the same limit the vacuum state approaches zero in the weak sense, as proposed by van Hove.