论文标题
背景独立精确的重态化
Background independent exact renormalisation
论文作者
论文摘要
Wilson精确的重量级化组的几何公式是基于规格不变的紫外线正规化方案而没有引入背景场的。这允许在连续体中采用明显的背景独立方法来实现量子重力和衡量理论。正则化是由Slavnov方案组成的几何变体，该方案由修改的动作组成，该动作抑制了高动量模式，并补充了路径积分中的Pauli-Villars决定因素。通过要求路径积分在截止量表的变化下，同时保留准分位置的情况下，可以得出Wilsonian有效作用的确切的重量量量量归量定组方程。重量量应该的流量直接定义在规格不变动作的空间上，而无需固定仪表。我们表明，可以在不固定仪表的情况下计算一环的一环beta函数，并且可以计算一般相对论的一环发差。作为第一个非扰动应用程序，我们在Wilsonian有效动作的简单截断中找到了Yang-Mills Beta功能的形式。
A geometric formulation of Wilson's exact renormalisation group is presented based on a gauge invariant ultraviolet regularisation scheme without the introduction of a background field. This allows for a manifestly background independent approach to quantum gravity and gauge theories in the continuum. The regularisation is a geometric variant of Slavnov's scheme consisting of a modified action, which suppresses high momentum modes, supplemented by Pauli-Villars determinants in the path integral measure. An exact renormalisation group flow equation for the Wilsonian effective action is derived by requiring that the path integral is invariant under a change in the cutoff scale while preserving quasi-locality. The renormalisation group flow is defined directly on the space of gauge invariant actions without the need to fix the gauge. We show that the one-loop beta function in Yang-Mills and the one-loop divergencies of General Relativity can be calculated without fixing the gauge. As a first non-perturbative application we find the form of the Yang-Mills beta function within a simple truncation of the Wilsonian effective action.
