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  Integral eigenvalues in compact rank-2 symmetric U(1) gauge theory

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I am reading a paper related to rank-2 symmetric $U(1)$ gauge theory: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.98.035111 (or on arXiv: https://arxiv.org/abs/1802.10108). My question concerns a skipped calculation in Sec. II. There, the authors wrote that $A_{\mu\nu}$ being compact (mod $2\pi$) and the canonical commutator $[A_{\mu\nu},E_{\mu\nu}]=-i$ implies that the eigenvalues of $E_{\mu\nu}$ are integers. I don't follow the authors reasoning here and I don't see why the eigenvalues should be integers. Would someone please enlighten me? Thanks!!

asked Dec 22, 2020 in Theoretical Physics by Waterfall (20 points) [ revision history ]

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