论文标题
保形网的量子操作
Quantum Operations on Conformal Nets
论文作者
论文摘要
在一个共形净$ \ MATHCAL {A} $上，可以考虑每个本地代数$ \ Mathcal {a}（i）$的Unital完全积极地图，以自然兼容性，真空保存和完整的协方差条件。我们在$ \ mathcal {a} $上称\ emph {量子操作}为“极端地图”的子集。 The usual automorphisms of $\mathcal{A}$ (the vacuum preserving invertible unital *-algebra morphisms) are examples of quantum operations, and we show that the fixed point subnet of $\mathcal{A}$ under all quantum operations is the Virasoro net generated by the stress-energy tensor of $\mathcal{A}$.此外，我们表明，每个不可约合的子网$ \ MATHCAL {B} \ subset \ Mathcal {a} $都是量子操作子集中的固定点。 当$ \ MATHCAL {B} \ subset \ Mathcal {a} $是离散的（或使用有限的Jones索引）时，我们表明，在$ \ Mathcal {a} $上的一组量子操作，它们留下$ \ Mathcal {b} $ element固定的compact（或有限）的结构。在相同的假设下，我们提供了中间保形网和封闭的亚脱落组之间的GALOIS对应关系。特别是，我们表明中间的保形网与中间子因子是一对一的对应关系，从而扩大了有限指数/完全合理的保形网络中Longo的结果[LON03]。
On a conformal net $\mathcal{A}$, one can consider collections of unital completely positive maps on each local algebra $\mathcal{A}(I)$, subject to natural compatibility, vacuum preserving and conformal covariance conditions. We call \emph{quantum operations} on $\mathcal{A}$ the subset of extreme such maps. The usual automorphisms of $\mathcal{A}$ (the vacuum preserving invertible unital *-algebra morphisms) are examples of quantum operations, and we show that the fixed point subnet of $\mathcal{A}$ under all quantum operations is the Virasoro net generated by the stress-energy tensor of $\mathcal{A}$. Furthermore, we show that every irreducible conformal subnet $\mathcal{B}\subset\mathcal{A}$ is the fixed points under a subset of quantum operations. When $\mathcal{B}\subset\mathcal{A}$ is discrete (or with finite Jones index), we show that the set of quantum operations on $\mathcal{A}$ that leave $\mathcal{B}$ elementwise fixed has naturally the structure of a compact (or finite) hypergroup, thus extending some results of [Bis17]. Under the same assumptions, we provide a Galois correspondence between intermediate conformal nets and closed subhypergroups. In particular, we show that intermediate conformal nets are in one-to-one correspondence with intermediate subfactors, extending a result of Longo in the finite index/completely rational conformal net setting [Lon03].
