There are several methods to regularize ultraviolet divergences, but among them, dimensional regularizationDimensional regularization [tHV72, Col84, Mut87] is the only method that allows systematically performing higher-order renormalization calculations while preserv ing diffeomorphism invariance.This is a method of making the theory finite by reduc ing space time dimension to less than 4, so that ultraviolet divergences are extracted as poles of \(D-4\) and renormalization calculations can be performed relatively easily. After removing ultraviolet divergences, return the dimension to 4 and find physical quantities. In this regularization method, information of the Wess-Zumino action S, which is the contribution from the path integral measure, is included in the D dimensional bare action.

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Renormalization Using Dimensional Regularization

  • Ken-ji Hamada

摘要

There are several methods to regularize ultraviolet divergences, but among them, dimensional regularizationDimensional regularization [tHV72, Col84, Mut87] is the only method that allows systematically performing higher-order renormalization calculations while preserv ing diffeomorphism invariance.This is a method of making the theory finite by reduc ing space time dimension to less than 4, so that ultraviolet divergences are extracted as poles of \(D-4\) and renormalization calculations can be performed relatively easily. After removing ultraviolet divergences, return the dimension to 4 and find physical quantities. In this regularization method, information of the Wess-Zumino action S, which is the contribution from the path integral measure, is included in the D dimensional bare action.