标题： 非对易几何中的格点微扰理论与三维非对易QED中的宇称异常 显示英文标题

标题： Lattice Perturbation Theory in Noncommutative Geometry and Parity Anomaly in 3D Noncommutative QED

摘要： 我们为非交换几何中的规范理论建立了格点微扰理论。 我们将它应用于三维非交换QED，并计算了由狄拉克费米子引起的有效作用量。 特别是，无质量理论的“宇称不变性”会受到异常影响，该异常由非交换陈-西蒙斯作用量表示。 异常的系数由一个依赖于格点作用量的整数标记，这是在交换理论中已知现象的非交换对应物。 也可以使用Ginsparg-Wilson费米子得到宇称异常，其中质量零在有限格点间距下得到保证。 这表明在非交换环面上对格点正则化的陈-西蒙斯理论有一个自然定义，这可能使量子霍尔系统的非微扰研究成为可能。 显示英文摘要

摘要： We formulate lattice perturbation theory for gauge theories in noncommutative geometry. We apply it to three-dimensional noncommutative QED and calculate the effective action induced by Dirac fermions. In particular "parity invariance" of a massless theory receives an anomaly expressed by the noncommutative Chern-Simons action. The coefficient of the anomaly is labelled by an integer depending on the lattice action, which is a noncommutative counterpart of the phenomenon known in the commutative theory. The parity anomaly can also be obtained using Ginsparg-Wilson fermions, where the masslessness is guaranteed at finite lattice spacing. This suggests a natural definition of the lattice-regularized Chern-Simons theory on a noncommutative torus, which could enable nonperturbative studies of quantum Hall systems.