什么是电荷？：相对论量子场论中作为局域可观测量的电荷
What is electric charge?: Charge as a local observable in relativistic quantum field theory
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中文总结 AI 辅助
本文针对相对论量子场论中电荷未被明确定义为局域可观测量的问题，基于 $C^{*}$-代数框架，提出范围局域电荷 $Q_{\boldsymbol{\nu}}(P)$ 的概念，回应电荷算符的局域化问题。
中文摘要 AI 辅助
现代量子物理学似乎并未对“什么是电荷”这一简单问题给出明确答案，这一情况相当令人惊讶。即便总电荷算符 $Q$ 定义明确，其非局域性意味着它并非通常意义上可通过（局域）实验装置测量的可观测量。电荷算符“局域版本”的候选者是四维电流算符 $j=(j^{\boldsymbol{\nu}})_{\boldsymbol{\nu}=0,1,2,3}$，但已知在 $(3+1)$ 维闵可夫斯基空间中，$j$ 的严格定义十分困难。尽管 Carey 等人已发现电流可在 $(1+1)$ 维空间中定义，本文作者认为，即便 $j$ 能被恰当定义，其作为“局域电荷算符”的可解释性仍存疑问。相反，本文回到 Araki 和 Wyss（1964）的研究，针对由有限维投影表示的“ scope（范围）”$P$，提出“ scope-local charge（范围局域电荷）”$Q_{\boldsymbol{\nu}}(P)$ 的概念，研究基于抽象 $C^{*}$-代数框架展开。
英文摘要
It is rather surprising that modern quantum physics does not appear to have provided any clear answer to the simple question ``what is electric charge?''. Even when the total charge operator $Q$ is well-defined, the non-locality of $Q$ implies that it is not an observable in the usual sense, which can be measured by a (local) experimental apparatus. A candidate for the ``local version'' of charge operator is the 4-current operator $j=(j^μ)_{μ=0,1,2,3}$. However, it is known that the rigorous definition of $j$ is difficult in $(3+1)$-dimensional Minkowski space. Although it was found that the current can be defined in $(1+1)$-dimensions (Carey et al.), I argue that even when $j$ can be suitably defined, the interpretability of $j$ as the ``local charge operator'' is dubious. Instead I return to Araki and Wyss (1964), and propose the concept of ``scope-local charge'' $Q_ζ(P)$ for a ``scope'' $P$, expressed by a finite-dimensional projection. I work in an abstract $C^{*}$-algebraic setting.
