Title: Nonlocal Yang-Mills Show Chinese title

Title: 非局域杨-米尔斯理论

Abstract: We present a very simple and explicit procedure for nonlocalizing the action of any theory which can be formulated perturbatively. When the resulting nonlocal field theory is quantized using the functional formalism --- with unit measure factor --- its Green's functions are finite to all orders. The construction also ensures perturbative unitarity to all orders for scalars with nonderivative interactions, however, decoupling is lost at one loop when vector and tensor quanta are present. Decoupling can be restored (again, to all orders) if a suitable measure factor exists. We compute the required measure factor for pure Yang-Mills at order $g^2$ and then use it to evaluate the vacuum polarization at one loop. A peculiar feature of our regularization scheme is that the on-shell tree amplitudes are completely unaffected. This implies that the nonlocal field theory can be viewed as a highly noncanonical quantization of the original, local field equations. Show Chinese abstract

Abstract: 我们提出了一种非常简单且明确的方法，用于非定域化任何可以摄动表述的理论的作用量。 当使用泛函形式主义（具有单位测度因子）对由此产生的非定域场论进行量子化时，其格林函数在所有阶次上都是有限的。 该构造还确保了标量的非导数相互作用在所有阶次上的微扰幺正性；然而，当存在向量和张量量子时，在一环处解耦丢失。 如果存在合适的测度因子，则可以恢复解耦（同样，在所有阶次上）。 我们在 $g^2$ 阶次计算了纯杨-米尔斯理论所需的测度因子，然后用它来评估一环真空极化。 我们的正则化方案的一个奇特之处在于，它的树图振幅在物理上完全不受影响。 这意味着非定域场论可以被视为原始局部场方程的一种高度非规范化的量子化。