  We consider domain walls obtained by embedding the 1+1-dimensional
$\phi^4$-kink in higher dimensions. We show that a suitably adapted dimensional
regularization method avoids the intricacies found in other regularization
schemes in both supersymmetric and non-supersymmetric theories. This method
allows us to calculate the one-loop quantum mass of kinks and surface tensions
of kink domain walls in a very simple manner, yielding a compact d-dimensional
formula which reproduces many of the previous results in the literature. Among
the new results is the nontrivial one-loop correction to the surface tension of
a 2+1 dimensional N=1 supersymmetric kink domain wall with chiral domain-wall
fermions.
