Ultraviolet divergence and Ward-Takahashi identity in a two-dimensional Dirac electron system with short-range impurities.

Dirac electrons in two-dimensional continuum space subject to &function impurities, which have inherent ultraviolet divergence, fail to be gauge-invariant if regularized by the standard momentum (Brillouin-zone) cutoff. A regularization scheme which respects gauge invariance is proposed here based on the cutoff in the impurity-potential range. The relation to a lattice model, which has no ultraviolet divergence, is also discussed. [ABSTRACT FROM AUTHOR]