1998/12/31 by David H. Adams
Physics and Astronomy · Mathematics · #hep-lat #hep-th #math-ph #math.MP
paper · pdf · doi:10.1006/aphy.2001.6209
published as Annals Phys. 296 (2002) 131-151 · Latex, 33 pages. v6: shortened and (hopefully) more succinct version, to appear in Ann.Phys
arxiv created 2001/10/04 · arxiv updated 2009/11/30
An explicit, detailed evaluation of the classical continuum limit of the axial anomaly/index density of the overlap Dirac operator is carried out in the infinite volume setting, and in a certain finite volume setting where the continuum limit involves an infinite volume limit. Our approach is based on a novel power series expansion of the overlap Dirac operator. The correct continuum expression is reproduced when the parameter m0 is in the physical region 0<m0<2. This is established for a broad range of continuum gauge fields. An analogous result for the fermionic topological charge, given by the index of the overlap Dirac operator, is then established for a class of topologically non-trivial fields in the aforementioned finite volume setting. Problematic issues concerning the index in the infinite volume setting are also discussed.