Topological Summation in Lattice Gauge Theory
Topological Summation in Lattice Gauge Theory
复制标题
格子规范理论中的拓扑求和
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
I. Hip
中科院分区：
文献类型：
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作者：
W. Bietenholz;I. Hip
在规范理论中，场的组态常常出现在不同的拓扑扇区中。在具有手征费米子的晶格正则化系统中，这些扇区可以通过参考阿蒂亚-辛格指数定理来定义。然而，如果用格点规范组态的局部更新来模拟这样的模型，蒙特卡罗历史往往会在一个扇区中停留许多步骤，特别是在精细格点上。因此，期望值只能在特定部门内衡量。在这里，我们提出了一个试点研究中的2味Schwinger模型，探讨方法的近似完整的结果为一个可观察的-对应于一个合适的总和在所有部门-基于数值测量在几个特定的拓扑部门。我们还探讨各种程序的拓扑敏感性的间接评估，从这样的拓扑限制测量。
In gauge theories the field configurations often occur in distinct topological sectors. In a lattice regularised system with chiral fermions, these sectors can be defined by referring to the Atiyah-Singer Index Theorem. However, if such a model is simulated with local updates of the lattice gauge configuration, the Monte Carlo history tends to get stuck in one sector for many steps, in particular on fine lattices. Then expectation values can be measured only within specific sectors. Here we present a pilot study in the 2-flavour Schwinger model which explores methods of approximating the complete result for an observable — corresponding to a suitable sum over all sectors — based on numerical measurements in a few specific topological sectors. We also probe various procedures for an indirect evaluation of the topological susceptibility, starting from such topologically restricted measurements.