Dimensional Regularization and Nuclear Potentials

Abstract

It is shown how nucleon-nucleon potentials can be defined in N dimensions, using dimensional regularization to continue amplitudes. This provides an easy way to separate out contact ($\delta$-function) terms arising from renormalization. An example is worked out several ways for the case of two scalar particles exchanged between nucleons, which involves a very simple loop calculation. This leads to a Feynman-parameterized representation for the nucleon-nucleon potential. Alternately, a dispersion representation can be developed leading to a different, though equivalent, form.