= U(1) charge
{c}
{title2=$Q\in\mathbb Z$}
For the <circle group> parameterized by $e^{i\theta}$ with period $2\pi$, a <one-dimensional representation> acts as $e^{i\theta}\mapsto e^{iQ\theta}$, and its <integer> label $Q$ is its charge. Periodicity forces $Q\in\mathbb Z$. A <tensor product representation> adds <U(1) charges>, a <dual representation> negates them, and restriction to the <finite cyclic group> generated by $e^{2\pi i/n}$ retains only $Q\bmod n$. <Integer> normalization must be fixed before discussing a largest finite <subgroup> left by a condensate.
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