自由标量场的动力学定域性
Dynamical locality of the free scalar field
摘要：
动力学定域性（英语：Dynamical locality）是一个局部协变物理理论的条件，主张定域物理的运动学和动力学概念一致。这个条件在[arXiv：1106.4785]中被引入，在那里它被证明与一个理论在不同时空中描述相同的物理学意味着什么的问题密切相关。在本文中，我们详细考虑了自由最小耦合Klein-Gordon场的例子，既作为经典理论又作为量子理论（使用Weyl代数和涂抹场方法）。结果表明，无论是经典的还是在量子场论中，大质量理论在所有时空维度$n\ge 2$中都服从动力学定域性，并且允许时空中有许多连通分量。相比之下，无质量理论在任何时空维度上都违反了动力学定域性，无论是在经典理论还是量子理论中，都是由于严格的规范对称性。考虑到这一点（等效地，与无质量电流一起工作），在连通时空上的所有维度上恢复了$n\ge 2$的动力学定域性，如果允许不连通时空，则在所有维度上恢复了$n\ge 3$的动力学定域性。量子化理论的结果得到了使用一般的结果给出的条件下，动态局部经典辛理论有动态局部量子化。
英文摘要：
Dynamical locality is a condition on a locally covariant physical theory, asserting that kinematic and dynamical notions of local physics agree. This condition was introduced in [arXiv:1106.4785], where it was shown to be closely related to the question of what it means for a theory to describe the same physics on different spacetimes. In this paper, we consider in detail the example of the free minimally coupled Klein--Gordon field, both as a classical and quantum theory (using both the Weyl algebra and a smeared field approach). It is shown that the massive theory obeys dynamical locality, both classically and in quantum field theory, in all spacetime dimensions $n\ge 2$ and allowing for spacetimes with finitely many connected components. In contrast, the massless theory is shown to violate dynamical locality in any spacetime dimension, in both classical and quantum theory, owing to a rigid gauge symmetry. Taking this into account (equivalently, working with the massless current) dynamical locality is restored in all dimensions $n\ge 2$ on connected spacetimes, and in all dimensions $n\ge 3$ if disconnected spacetimes are permitted. The results on the quantized theories are obtained using general results giving conditions under which dynamically local classical symplectic theories have dynamically local quantizations.
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