有限群量子偶中不可区分的电荷流对
Indistinguishable Chargeon-Fluxion Pairs in the Quantum Double of Finite Groups
摘要：
我们考虑有限群的量子偶的有限维表示范畴作为模张量范畴。我们研究了这一范畴的自等价，它在简单对象（粒子）集合上的诱导置换是PJ的特殊形式，其中J使每个粒子都处于它的电荷共轭，P是一个电荷流对的转置.我们证明了，如果基础群是有限域的加法群和乘法群的半直积，则存在这样的自等价。特别地，我们证明了对于S_3（三字母置换群），存在一个不可区分的电荷子和一个不可区分的流子。相反，通过考虑这样的置换作为模不变量，我们表明，换位的电荷流对形成一个模不变量，当且仅当相应的组是同构的半直积的加法和乘法组的有限近场。
英文摘要：
We consider the category of finite dimensional representations of the quantum double of a finite group as a modular tensor category. We study auto-equivalences of this category whose induced permutations on the set of simple objects (particles) are of the special form of PJ, where J sends every particle to its charge conjugation and P is a transposition of a chargeon-fluxion pair. We prove that if the underlying group is the semidirect product of the additive and multiplicative groups of a finite field, then such an auto-equivalence exists. In particular, we show that for S_3 (the permutation group over three letters) there is a chargeon and a fluxion which are not distinguishable. Conversely, by considering such permutations as modular invariants, we show that a transposition of a chargeon-fluxion pair forms a modular invariant if and only if the corresponding group is isomorphic to the semidirect product of the additive and multiplicative groups of a finite near-field.
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