标题： 格点上Ginsparg-Wilson费米子的指标定理准则 显示英文标题

标题： A Criterion for the Index Theorem on the Lattice with Ginsparg-Wilson Fermions

摘要： 在这里，我们研究从连续体到有限格点和有限拓扑电荷密度的指数定理可以推广多远。 为了检验威尔逊作用量如何近似指数定理，我们专注于施温格模型的格点版本。 我们还验证了纽伯格重叠作用量完全符合指数定理，并表明一种新的简单作用量对规范配置的拓扑结构是无感知的。 我们研究了吉尔斯帕格-威尔逊关系的解如何将威尔逊作用量的本征值投影到复平面上的圆上。 最后，我们提出了一种基于威尔逊作用量构建的吉尔斯帕格-威尔逊关系解的新标准。 我们得出结论，纽伯格作用量是与指数定理最大符合的最简单作用量，在d=2时其最佳参数为m0=1.1 +-p 0.1 。 显示英文摘要

摘要： Here we study how far the Index Theorem can be extrapolated from the continuum to finite lattices with finite topological charge densities. To examine how the Wilson action approximates the Index theorem, we specialize in the lattice version of the Schwinger model. We also verify that the Neuberger overlap action exactly complies with the Index theorem, and show that a new simple action is blind to the topology of the gauge configuration. We study how the solutions of the Ginsparg-Wilson Relation project the eigenvalues of the Wilson action to a circle in the complex Argand plane. Finally we propose a new criterion for solutions of the Ginsparg-Wilson Relation constructed with the Wilson action. We conclude that the Neuberger action is the simplest one that maximally complies with the Index Theorem, and that its best parameter in d=2 is m0=1.1 +-p 0.1 .