Regularization, Renormalization, and Dimensional Analysis: Dimensional Regularization meets Freshman E&M

Abstract

We illustrate the dimensional regularization technique using a simple problem from elementary electrostatics. We contrast this approach with the cutoff regularization approach, and demonstrate that dimensional regularization preserves the translational symmetry. We then introduce a Minimal Subtraction (MS) and a Modified Minimal Subtraction (MS-Bar) scheme to renormalize the result. Finally, we consider dimensional transmutation as encountered in the case of compact extra-dimensions.

Comments: LaTeX 7 pages. This work is based on lectures presented at the CTEQ Summer School on QCD Analysis and Phenomenology. Version 2 includes updates to match published version, and an enhanced appendix