标题： 从可观测量和状态到希尔伯特空间再回到希尔伯特空间：一个二范畴伴随 显示英文标题

标题： From observables and states to Hilbert space and back: a 2-categorical adjunction

摘要： 给定一个C*-代数的表示，视为物理可观测量的抽象集合，以及一个归一化的向量，通过限制可以得到该代数上的一个状态。 此构造相对于代数的变化是函子性的，其中两个特殊情况是对称性和包含关系。 我们证明这种限制有一个左伴随，即Gelfand-Naimark-Segal (GNS) 构造。 尽管在普通范畴中这样的伴随不存在，但在合适的2-范畴中存在。 每一个数学定义和结果之后都跟着一个物理解释。 显示英文摘要

摘要： Given a representation of a C*-algebra, thought of as an abstract collection of physical observables, together with a normalized vector, one obtains a state on the algebra via restriction. This construction is functorial with respect to alterations of the algebra, two special cases of which are symmetries and inclusions. We show that this restriction has a left adjoint given by the Gelfand-Naimark-Segal (GNS) construction. Although, such an adjoint does not exist in an ordinary category, it does in a suitable 2-category. Every mathematical definition and result is followed by a physical interpretation.