标题： 广义Ginsparg-Wilson代数和格点上的指标定理 显示英文标题

标题： Generalized Ginsparg-Wilson algebra and index theorem on the lattice

摘要： 最近对一类一般格点狄拉克算子的拓扑性质的研究被报道了。 这是基于一种特定的代数实现形式，即$\gamma_{5}(\gamma_{5}D)+(\gamma_{5}D)\gamma_{5} = 2a^{2k+1}(\gamma_{5}D)^{2k+2}$，其中$k$表示一个非负整数。 选择$k=0$对应于通常讨论的吉姆斯帕格-威尔森关系，从而对应于重叠算子。 结果显示，所有这些算子的局部手征异常和与瞬子相关的指标是相同的。 在零规范场情况下，所有这些狄拉克算子的局域性是基于显式构造证明的，但具有动态规范场的局域性尚未被建立。 我们建议威尔逊有效作用量对于避免一般微扰分析中遇到的红外奇异性是必不可少的。 显示英文摘要

摘要： Recent studies of the topological properties of a general class of lattice Dirac operators are reported. This is based on a specific algebraic realization of the Ginsparg-Wilson relation in the form $\gamma_{5}(\gamma_{5}D)+(\gamma_{5}D)\gamma_{5} = 2a^{2k+1}(\gamma_{5}D)^{2k+2}$ where $k$ stands for a non-negative integer. The choice $k=0$ corresponds to the commonly discussed Ginsparg-Wilson relation and thus to the overlap operator. It is shown that local chiral anomaly and the instanton-related index of all these operators are identical. The locality of all these Dirac operators for vanishing gauge fields is proved on the basis of explicit construction, but the locality with dynamical gauge fields has not been established yet. We suggest that the Wilsonian effective action is essential to avoid infrared singularities encountered in general perturbative analyses.