不同最高权下Diff $^+(S^1)$表示的局部等价性
Local equivalence of representations of Diff$^+(S^1)$ corresponding to different highest weights
摘要：
设$c,h$和$c,\tilde{h}$是${\rm Diff}^+(S^1)$的两个容许的中心电荷和最高权对。证明了群${\rm Diff}^+(S^1)$的正能量不可约投射酉表示$U_{c,h}$和$U_{c,\tilde{h}}$是局部等价的.这意味着，对于任何$I\Subset S^1$开真区间，存在酉算子$W_I$，使得对于所有作用于$I^c\equiv S^1\setminus I$的$γ\in {\rm Diff}^+(S^1)$，$W_I U_{c,h}(γ)W_I^* = U_{c,\tilde{h}}(γ)$（即只能“置换”或“移动”$I$中的点）。这一结果扩展和完成了早期的只处理某些区域的“$c,h$ -平面”，并关闭了Virasoro网的超选择部门的完整分类的差距。
英文摘要：
Let $c,h$ and $c,\tilde{h}$ be two admissible pairs of central charge and highest weight for ${\rm Diff}^+(S^1)$. It is shown here that the positive energy irreducible projective unitary representations $U_{c,h}$ and $U_{c,\tilde{h}}$ of the group ${\rm Diff}^+(S^1)$ are locally equivalent. This means that for any $I\Subset S^1$ open proper interval, there exists a unitary operator $W_I$ such that $W_I U_{c,h}(γ)W_I^* = U_{c,\tilde{h}}(γ)$ for all $γ\in {\rm Diff}^+(S^1)$ which act identically on $I^c\equiv S^1\setminus I$ (i.e. which can "displace" or "move" points only in $I$). This result extends and completes earlier ones that dealt with only certain regions of the "$c,h$-plane", and closes the gap in the full classification of superselection sectors of Virasoro nets.
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