论文标题
QFT中的广义对称性和Noether定理
Generalized symmetries and Noether's theorem in QFT
论文作者
论文摘要
我们表明，在具有noether电流的连续全局对称性下，广义对称性无法充电。此外，在连续的全局对称性下只能充电非紧缩的广义对称性。这些结果来自对扭曲操作员的分类，该分类自然扩展到有限的组全球对称性。他们在QFT中揭示了Noether定理的强大版本的拓扑障碍，即使在一般条件下，全球对称性可以通过Twist Operators在本地实施（弱版本）。我们将这些结果用于局部QFT中的Weinberg-Witten定理，将其推广到Lorentz组的任意维度和表示中的无质量粒子。描述了几个局部曲折但没有诺伊尔电流的例子。我们最终讨论了具有强大版本的条件，QFT的动力学方面与非紧密的广义对称性，比例与QFT中的保形不变性，与Coleman-Mandula定理的连接以及量子重力中全球对称性的方面。
We show that generalized symmetries cannot be charged under a continuous global symmetry having a Noether current. Further, only non-compact generalized symmetries can be charged under a continuous global symmetry. These results follow from a finer classification of twist operators, which naturally extends to finite group global symmetries. They unravel topological obstructions to the strong version of Noether's theorem in QFT, even if under general conditions a global symmetry can be implemented locally by twist operators (weak version). We use these results to rederive Weinberg-Witten's theorem within local QFT, generalizing it to massless particles in arbitrary dimensions and representations of the Lorentz group. Several examples with local twists but without Noether currents are described. We end up discussing the conditions for the strong version to hold, dynamical aspects of QFT's with non-compact generalized symmetries, scale vs conformal invariance in QFT, connections with the Coleman-Mandula theorem and aspects of global symmetries in quantum gravity.
