标题： 规范理论和引力中的半有限冯·诺依曼代数 显示英文标题

标题： Semifinite von Neumann algebras in gauge theory and gravity

摘要： 冯·诺依曼代数在规范理论和引力的背景下扮演着越来越重要的角色。 通过交换定理，交叉积提供了一种自然的方法来实现约束，使其成为构造规范不变代数的一个有用的工具。 一个III型代数与其模自同构群的交叉积是半有限的，这意味着交叉积调节了局部量子场论中的发散。 在这封信中，我们找到了一个充分条件，用于确定一个III型代数与包含模自同构群的任意局部紧致群的交叉积的半有限性。 我们的条件意外地表明了模流在对称群中的中心性，并且我们提供了该条件必要性的证据。 在这些条件下，我们构造了一个相关的迹线，用于计算物理期望值。 我们评论了这个结果的重要性及其对规范理论和引力中子区域物理学的影响。 显示英文摘要

摘要： von Neumann algebras have been playing an increasingly important role in the context of gauge theories and gravity. The crossed product presents a natural method for implementing constraints through the commutation theorem, rendering it a useful tool for constructing gauge invariant algebras. The crossed product of a Type III algebra with its modular automorphism group is semifinite, which means that the crossed product regulates divergences in local quantum field theories. In this letter, we find a sufficient condition for the semifiniteness of the crossed product of a type III algebra with any locally compact group containing the modular automorphism group. Our condition surprisingly implies the centrality of the modular flow in the symmetry group, and we provide evidence for the necessity of this condition. Under these conditions, we construct an associated trace which computes physical expectation values. We comment on the importance of this result and and its implications for subregion physics in gauge theory and gravity.