Renormalization Group in Potential Scattering

Renormalization group equations for the physical $t$ matrix are written for quantum scattering with some potentials singular at the origin in two and three dimensions. The momentum-space perturbative treatment of these scattering problems exhibits ultraviolet divergences and permits renormalization leading to a scale. These equations yield the correct asymptotic behavior and some low-energy properties of the $t$ matrix. Illustrations are made for the Dirac delta potential in two and three dimensions.