Renormalization using domain wall regularization

We formulate the renormalization procedure using the domain wall regularization that is based on the heat-kernel method. The quantum effects of both fermions and bosons (gauge fields) are taken into account. The background field method is quite naturally introduced. With regard to the treatment of the loop-momentum integrals, an interesting contrast between the fermion-determinant part and other parts is revealed. These points are elucidated by considering some examples. The Weyl anomalies for 2D QED and 4D QED are correctly obtained. It is found that the "chiral solution" produces (1/2)(d/2) X "correct values", where d is the spatial dimension. Considering the model of 2D QED, both Weyl and chiral anomalies are directly obtained from the effective action. The mass and wave function renormalization are explicitly performed in 4D QED. We confirm the multiplicative (not additive) renormalization, which demonstrates the advantage of no fine-tuning. The relation with the recently popular higher-dimensional approach, such as the Randall-Sundrum model, is commented on.