n Distinguishable Particles on the Real Line interacting via Two Body Delta Potentials

This paper studies a system of $n\in \mathbb{N}:n\ge 2$ non-relativistic, spinless quantum particles moving on the real line and interacting via a two-body delta potential. The Hamiltonian of such a system is proved to be affiliated to the resolvent algebra of the case, $\mathcal{R}({\mathbb{R}}^{2n},\sigma )$; it is further shown the existence of a ${\text{C}}^{\ast }-$dynamical system and of a subalgebra ${\pi }_S{\left({\mathfrak{S}}_0\right)}^{-1}\subset \mathcal{R}({\mathbb{R}}^{2n},\sigma )$, stable under time evolution, where ${\pi }_S$ is the Schr{ö}dinger representation of the algebra.