标题： 非阿贝尔有限元规范理论的准局部表述 显示英文标题

标题： Quasi-Local Formulation of Non-Abelian Finite-Element Gauge Theory

摘要： 最近已表明如何通过规范自由格点差分方程并同时确定规范变换的形式来表述非阿贝尔规范理论的有限元运动方程。特别是，以路径排序的指数（链路算符）乘积显式构造了规范协变的场强。另一方面，狄拉克和杨-米尔斯方程是非局域的，涉及整个先前格点的求和。早前，松山提出了一个由上述链路算符构建的局域狄拉克方程。在这里，我们展示了他的方案（与我们早期的方案密切相关）如何可以用于非阿贝尔规范理论。尽管狄拉克和杨-米尔斯方程现在是局域的，但场强不是。该技术通过二维和四维时空中的电流反常的直接计算进行了说明。不幸的是，与最初的有限元提议不同，这个方案一般是非幺正的。 显示英文摘要

摘要： Recently it was shown how to formulate the finite-element equations of motion of a non-Abelian gauge theory, by gauging the free lattice difference equations, and simultaneously determining the form of the gauge transformations. In particular, the gauge-covariant field strength was explicitly constructed, locally, in terms of a path ordered product of exponentials (link operators). On the other hand, the Dirac and Yang-Mills equations were nonlocal, involving sums over the entire prior lattice. Earlier, Matsuyama had proposed a local Dirac equation constructed from just the above-mentioned link operators. Here, we show how his scheme, which is closely related to our earlier one, can be implemented for a non-Abelian gauge theory. Although both Dirac and Yang-Mills equations are now local, the field strength is not. The technique is illustrated with a direct calculation of the current anomalies in two and four space-time dimensions. Unfortunately, unlike the original finite-element proposal, this scheme is in general nonunitary.