晶格上的能量动量张量：杨-米尔斯理论中的非微扰重整化
Energy-momentum tensor on the lattice: non-perturbative renormalization in Yang--Mills theory
摘要：
我们在晶格上构造了一个能量动量张量，它满足适当的沃德恒等式（WI），并且在连续极限具有右迹反常。它是通过施加与连续统理论的庞加莱不变性相关联的适当WI来定义的。当盒子在时间方向上的长度是有限的时候，这些关系就出现了，如果坐标轴和周期轴不对齐，它们就采取一种特别简单的形式。我们实现了SU（3）杨-米尔斯理论离散与标准的威尔逊作用量在（短）时间方向移动的边界条件的存在下的方法。通过进行大量的数值模拟，张量的无痕分量的重整化常数被确定，对于裸耦合常数的值在0<= g^2_0<=1的范围内，其精度大约为0.5%。
英文摘要：
We construct an energy-momentum tensor on the lattice which satisfies the appropriate Ward Identities (WIs) and has the right trace anomaly in the continuum limit. It is defined by imposing suitable WIs associated to the Poincare` invariance of the continuum theory. These relations come forth when the length of the box in the temporal direction is finite, and they take a particularly simple form if the coordinate and the periodicity axes are not aligned. We implement the method for the SU(3) Yang--Mills theory discretized with the standard Wilson action in presence of shifted boundary conditions in the (short) temporal direction. By carrying out extensive numerical simulations, the renormalization constants of the traceless components of the tensor are determined with a precision of roughly half a percent for values of the bare coupling constant in the range 0<= g^2_0<=1.
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