%0 Journal Article %1 Chiu1998 %A Chiu, Ting-Wai %D 1998 %K ChiralSymmetry GinspargWilson IndexTheorem %T Topological Charge and The Spectrum of Exactly Massless Fermions on the Lattice %U http://arxiv.org/abs/hep-lat/9804016 %X The square root of the positive definite hermitian operator $D_w^\dagger D_w$ in Neuberger's proposal of exactly massless quarks on the lattice is implemented by the recursion formula $Y_k+1 = 1/2 (Y_k + D_w^\dagger D_w Y_k^-1)$ with $Y_0 = \Id$, where $Y_k^2$ converges to $D_w^\dagger D_w$ quadratically. The spectrum of the lattice Dirac operator for single massless fermion in two dimensional background U(1) gauge fields is investigated. For smooth background gauge fields with non-zero topological charge, the exact zero modes with definite chirality are reproduced to a very high precision on a finite lattice and the Index Theorem is satisfied exactly. The fermionic determinants are also computed and they are in good agreement with the continuum exact solution.

@article{Chiu1998, abstract = { The square root of the positive definite hermitian operator $D_w^{\dagger} D_w$ in Neuberger's proposal of exactly massless quarks on the lattice is implemented by the recursion formula $Y_{k+1} = {1/2} (Y_k + D_w^{\dagger} D_w Y_k^{-1})$ with $Y_0 = \Id$, where $Y_k^2$ converges to $D_w^{\dagger} D_w$ quadratically. The spectrum of the lattice Dirac operator for single massless fermion in two dimensional background U(1) gauge fields is investigated. For smooth background gauge fields with non-zero topological charge, the exact zero modes with definite chirality are reproduced to a very high precision on a finite lattice and the Index Theorem is satisfied exactly. The fermionic determinants are also computed and they are in good agreement with the continuum exact solution. }, added-at = {2010-03-19T11:25:36.000+0100}, author = {Chiu, Ting-Wai}, biburl = {https://www.bibsonomy.org/bibtex/225f7e277f425287cc0e278c4ee4f0e02/gber}, description = {[hep-lat/9804016] Topological Charge and The Spectrum of Exactly Massless Fermions on the Lattice}, interhash = {cba2ade7bc4d6392f4f639ac0e1ed0d9}, intrahash = {25f7e277f425287cc0e278c4ee4f0e02}, keywords = {ChiralSymmetry GinspargWilson IndexTheorem}, note = {cite arxiv:hep-lat/9804016 Comment: 18 pages (LaTeX), 2 figures (EPS)}, timestamp = {2010-03-19T11:25:36.000+0100}, title = {Topological Charge and The Spectrum of Exactly Massless Fermions on the Lattice}, url = {http://arxiv.org/abs/hep-lat/9804016}, year = 1998 }