The Wightman axioms and the mass gap for strong interactions of exponential type in two-dimensional space-time

We construct boson models in two space-time dimensions which satisfy all the Wightman axioms with mass gap. The interactions are exponential and no restriction on the size of the coupling constant is made. The Schwinger functions for the space cut-off interaction are shown to be non-negative and to decrease monotonically to their unique, non zero, infinite volume limit, as the space cut-off is removed. The correspondent Wightman functions satisfy all the Wightman axioms. The mass gap of the space cut-off Hamiltonian is non decreasing as the space cut-off is removed and the Hamiltonian for the infinite volume limit has mass gap at least as large as the bare mass. The infinite volume Schwinger functions and the mass gap depend monotonically on the coupling constant and the bare mass. The coupling of the first power of the field to the first excited state is proven and an equation of motion for the interacting field is derived.