Block-spin transformations from a fine lattice to a coarse one are shown to give rise to a one-to-one correspondence between the zero-modes of the Ginsparg-Wilson Dirac operator on the fine lattice and those on the coarse lattice. The index is then preserved under the blocking process. Such a one-to-one correspondence is violated and the block-spin transformation becomes necessarily ill-defined when the absolute value of the index is larger than 2rN, where N is the number of the sites on the coarse lattice and r is the dimension of the gauge group representation of the fermion variables. (C) 2000 Elsevier Science B.V.
|Number of pages||7|
|Journal||Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics|
|Publication status||Published - Sep 7 2000|
All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics