Simple Evaluation of the Chiral Jacobian with the Overlap Dirac Operator

The chiral Jacobian, which is defined with Neuberger’s overlap Dirac operator of the lattice fermion, is explicitly evaluated in the continuum limit without expanding it in the gauge coupling constant. Our calculational scheme is simple and straightforward. We determine a coefficient of the chiral anomaly for general values of the mass parameter and the Wilson parameter of the overlap Dirac operator. ⋆ E-mail: [email protected] In a recent studies of the chiral symmetries on a lattice, the lattice chiral Jacobian [1,2] ln J = −2ia ∑ x α(x) tr γ5 [ 1− 1 2 aD(x) ] δ(x, y) ∣∣∣∣ y=x , δ(x, y) = 1 a4 δx,y, (1) associated with the Dirac operator D(x) which satisfies the Ginsparg-Wilson relation [3] D(x)γ5 + γ5D(x) = aD(x)γ5D(x), (2) plays a central role. The simplest example of such a D(x) is given by the overlap Dirac operator [4,5],