One Dimensional Point Interactions and the Resolvent Algebra -- Simple Remarks

This paper shows that the resolvent algebra $\mathcal{R}({\mathbb{R}}^2,\sigma )$ can accommodate dynamics induced by self-adjoint Hamiltonians on $L^2\left(\mathbb{R}\right)$ describing a single non-relativistic spinless particle undergoing one up to countably many different fixed point interactions located on the real line.