Chiral anomaly for a new class of lattice Dirac operators Original Research Article

A new class of lattice Dirac operators which satisfy the index theorem have been recently proposed on the basis of the algebraic relation γ5(γ5D)+(γ5D)γ5=2a2k+1(γ5D)2k+2 . Here k stands for a non-negative integer and k=0 corresponds to the ordinary Ginsparg–Wilson relation. We analyze the chiral anomaly and index theorem for all these Dirac operators in an explicit elementary manner. We show that the coefficient of anomaly is independent of a small variation in the parameters r and m0 , which characterize these Dirac operators, and the correct chiral anomaly is obtained in the (naive) continuum limit a→0 .