TOPOLOGICAL CHARGE AND THE SPECTRUM OF EXACTLY MASSLESS FERMIONS ON THE LATTICE - ART. NO. 074511

The square root of the positive definite Hermitian operator (DwDw)-D-d agger in Neuberger's proposal of exactly massless quarks on the lattic e is implemented by the recursion formula Yk+1 = 1/2(Y-k + (DwDwYk-1)- D-dagger) with Y-0 = 1, where Y-k(2) converges to (DwDw)-D-dagger quad ratically. The spectrum of the lattice Dirac operator for single massl ess fermion in two dimensional background U(1) gauge fields is investi gated. For smooth background gauge fields with nonzero topological cha rge, the exact zero modes with definite chirality are reproduced to a very high precision on a finite lattice and the index theorem is satis fied exactly. The fermionic determinants are also computed and they ar e in good agreement with the continuum exact solution. [S0556-2821(98) 04519-6].