Lattice representation of vector and chiral gauge theories
  A lattice derivative is defined as a discrete Fourier transform of momentum on a finite lattice. Species doublers are removed with anti-periodic boundary conditions. U(1) chiral transformation is modified to reproduce chiral anomaly. Chiral gauge theories can be constructed on the lattice using a single Weyl fermion as a building block. 
Takanori Sugihara (RIKEN BNL)