General bounds on the Wilson-Dirac operator
Adams, David H.
Date of Issue2003
School of Physical and Mathematical Sciences
Lower bounds on the magnitude of the spectrum of the Hermitian Wilson-Dirac operator H(m) have previously been derived for 0<m<2 when the lattice gauge field satisfies a certain smoothness condition. In this paper lower bounds are derived for 2p-2<m<2p for general p=1,2,…,d where d is the spacetime dimension. The bounds can alternatively be viewed as localization bounds on the real spectrum of the usual Wilson-Dirac operator. They are needed for the rigorous evaluation of the classical continuum limit of the axial anomaly and the index of the overlap Dirac operator at general values of m, and provide information on the topological phase structure of overlap fermions. They are also useful for understanding the instanton size dependence of the real spectrum of the Wilson-Dirac operator in an instanton background.
Physical and Mathematical Sciences
Physical review D
© 2003 The American Physical Society. This paper was published in Physical Review D and is made available as an electronic reprint (preprint) with permission of The American Physical Society. The paper can be found at the following official DOI: http://dx.doi.org/10.1103/PhysRevD.68.065009. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.