标题： 格点上满足吉纳斯帕格-威尔逊关系的指标定理的一个准则 显示英文标题

标题： A Criterium for the Index Theorem on the Lattice with the Ginsparg Wilson Relation

摘要： Ginsparg Wilson 关系和 Neuberger 动力学最近改善了对格点上指标定理的理解，然而这个问题尚未解决。 利用目前可用的标准，我们开发了一种基于根和极点位置的技术，以构建 Ginsparg Wilson 关系的新简单解。 在自由费米子的情况下，我们研究了 Wilson 动力学、简单动力学和 Neuberger 动力学的根、极点和局部性。 然后我们探讨了拓扑规范构型对不同动力学本征值的影响。 在 Schwinger 模型的离散版本中，我们检查了 GWR 解如何将 Wilson 动力学的本征值投影到复数 Argand 平面上的圆上。 最后我们提出了一个由 Wilson 动力学构建的 Ginsparg Wilson 关系的新标准。 我们得出结论，Neuberger 动力学是符合指标定理的最简单动力学，最佳参数为 m0=1.1 +-p 0.1 。 显示英文摘要

摘要： The Ginsparg Wilson Relation and the Neuberger action recently improved the understanding of the Index Theorem on the lattice, however this problem has not been solved yet. With the presently available criteria, we develop a technique based on the position of roots and poles to build a new simple solution of the Ginsparg Wilson Relation. In the free fermion case, we study the roots, the poles, and the locality of the Wilson action, the simple action and the Neuberger action. Then we explore the effects of topological gauge configurations on the eigenvalues of the different actions. In the discrete version of the Schwinger model we examine how the GWR solutions project the eigenvalues of the Wilson action to a circle in the complex Argand plane. Finally we propose a new criterium for solutions of the Ginsparg Wilson Relation constructed with the Wilson action. We conclude that the Neuberger action is the simplest one that complies with the Index Theorem, and that the best parameter is m0=1.1 +-p 0.1 .