THE FERMIONIC MATRIX, INSTANTONS, ZERO MODES AND MULTIGRID

We apply multigrid (MG) concepts to the problem of estimating the fermionic determinant. MG is used both as an analysis guide and as calculational tool. The MG analysis emphasizes the role of the "approximate zero modes" (AZM) in the slowing down of the process. We demonstrate that in the case of a single AZM the MG allows the estimation of the inverse matrix for K-S fermions with no slowing down. The connection between the total topological charge Qtot and the convergence rate is striking. While the convergence rate in a straightforward two-level "experiment" is poor for one smooth instanton (Qtot = 1), it is good for an instanton-anti-instanton (Qtot = 0), irrespective of their relative distance. © 1980.