2026/08/01 by Hideyasu Yamashita
Physics and Astronomy · #quant-ph #msc:81T05 #msc:81P05
16 pages
arxiv created 2026/08/01 · arxiv updated 2026/08/04
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=(jμ)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'' Qζ(P) for a ``scope'' P, expressed by a finite-dimensional projection. I work in an abstract C*-algebraic setting.