标题： 弯曲时空中的量子场论的Coleman-Mandula定理的类似物 显示英文标题

标题： An analogue of the Coleman-Mandula theorem for quantum field theory in curved spacetimes

摘要： 科勒曼-曼杜拉（CM）定理指出，闵可夫斯基时空量子场论的庞加莱对称性和内部对称性不能在扩展对称群中非平凡地结合。 我们建立了在弯曲时空中的量子场论的类似结果，假设局部协变性、时间片性质、洛伦兹不变性的局部动力形式以及可加性。 与CM定理不同，我们的结果适用于维度$n\ge 2$并且适用于自由或相互作用理论。 它适用于定义在一个所有全局双曲时空范畴上的理论，这些时空配备了一个全局余标架，受限洛伦兹群在其上作用，并利用了由群$G$在时空范畴上的作用引起的对称性的普遍分析。 这些对称性被证明与$G$的二阶非阿贝尔上同调群中一个上同调类有自然联系，系数为理论的全局规范群。 我们的主要结果证明，如果$G$是受限洛伦兹群的万有覆盖$\cal S$，则该上同调类是平凡的。 作为其他结果之一，可以得出扩展对称群是全局规范群和$\cal S$的直积，所有场都以$\cal S$的多重态形式变换，在扩展群下不同自旋的场不会混合，非整数自旋的出现由全局规范群的中心控制。 该普遍分析也应用于刚性尺度协变性。 显示英文摘要

摘要： The Coleman-Mandula (CM) theorem states that the Poincar\'e and internal symmetries of a Minkowski spacetime quantum field theory cannot combine nontrivially in an extended symmetry group. We establish an analogous result for quantum field theory in curved spacetimes, assuming local covariance, the timeslice property, a local dynamical form of Lorentz invariance, and additivity. Unlike the CM theorem, our result is valid in dimensions $n\ge 2$ and for free or interacting theories. It is formulated for theories defined on a category of all globally hyperbolic spacetimes equipped with a global coframe, on which the restricted Lorentz group acts, and makes use of a general analysis of symmetries induced by the action of a group $G$ on the category of spacetimes. Such symmetries are shown to be canonically associated with a cohomology class in the second degree nonabelian cohomology of $G$ with coefficients in the global gauge group of the theory. Our main result proves that the cohomology class is trivial if $G$ is the universal cover $\cal S$ of the restricted Lorentz group. Among other consequences, it follows that the extended symmetry group is a direct product of the global gauge group and $\cal S$, all fields transform in multiplets of $\cal S$, fields of different spin do not mix under the extended group, and the occurrence of noninteger spin is controlled by the centre of the global gauge group. The general analysis is also applied to rigid scale covariance.