局部协变量子场论的自同态与自同构
Endomorphisms and automorphisms of locally covariant quantum field theories
摘要：
在局部协变量子场论的框架中，理论被描述为从时空范畴到 *-代数范畴的函子。提出了这样一个理论的整体规范群可以被识别为定义函子的自同构群。因此，多重域可以在函子层次上被识别。它表明，服从Minkowski空间中的标准假设的局部协变理论，包括能量紧性，没有适当的自同态（即，所有的自同态都是自同构）并且具有紧自同构群。此外，它是如何显示的自同态和自同构的局部协变理论可能，在原则上，在任何单一的时空进行分类。作为一个例子，我们对一个多自由标量场系统的自同态和自同构进行了完全分类。
英文摘要：
In the framework of locally covariant quantum field theory, a theory is described as a functor from a category of spacetimes to a category of *-algebras. It is proposed that the global gauge group of such a theory can be identified as the group of automorphisms of the defining functor. Consequently, multiplets of fields may be identified at the functorial level. It is shown that locally covariant theories that obey standard assumptions in Minkowski space, including energy compactness, have no proper endomorphisms (i.e., all endomorphisms are automorphisms) and have a compact automorphism group. Further, it is shown how the endomorphisms and automorphisms of a locally covariant theory may, in principle, be classified in any single spacetime. As an example, the endomorphisms and automorphisms of a system of finitely many free scalar fields are completely classified.
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