Local chiral symmetry for gauge theories on wilson’s lattice

Summary  With the problem of chiral symmetry on the Wilson lattice in space-time as an objective, we introduce a definition of differentiation on a lattice which respects the product rule of Leibnitz d(fg)=f dg+(df)g for functionsf, g. The derivative is essentially a generalization of the SLAC derivative on a lattice. With this derivative, chiral (symmetry) currents have all the characteristics that they possess in the continuum quantum theory of fields. In particular, the Adler-Bell-Jackiw anomaly theorem has the same form as in the continuum.