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

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

2008-12-18

arxiv.org/abs/0812.3578v1

Physics

High Energy Physics

High Energy Physics - Phenomenology

LaTeX 7 pages. This work is based on lectures presented at the CTEQ Summer School on QCD Analysis and Phenomenology

Scientific paper

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.

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