arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2103.08409gr-qchep-th
收藏

圈量子引力的边界映射

Loop Quantum Gravity's Boundary Maps

Qian Chen, Etera R. Livine

摘要:

在正则量子引力中,空间边界的存在自然导致边界量子态,代表体场的量子边界条件。因此,体几何的量子态需要升级为在边界希尔伯特空间中取值的波函数:体成为作用于边界态的量子算符。我们将其应用到圈量子引力中,并将具有二维边界的自旋网络描述为将体完整性映射到边界上的自旋态的波函数。这在一个清晰的数学框架中设置了体-边界关系,其允许在追踪出体自由度之后定义由体自旋网络状态引起的边界密度矩阵。我们问的问题的散装重建,并证明了一个边界到散装普遍的重建过程,被理解为一个净化的混合边界状态到一个纯粹的散装状态。我们进一步执行的诱导边界密度矩阵的代数结构的第一次调查,并显示如何体激发,即量子的三维几何形状之间的相关性,得到反映到边界密度矩阵。

英文摘要:

In canonical quantum gravity, the presence of spatial boundaries naturally leads to a boundary quantum states, representing quantum boundary conditions for the bulk fields. As a consequence, quantum states of the bulk geometry needs to be upgraded to wave-functions valued in the boundary Hilbert space: the bulk become quantum operator acting on boundary states. We apply this to loop quantum gravity and describe spin networks with 2d boundary as wave-functions mapping bulk holonomies to spin states on the boundary. This sets the bulk-boundary relation in a clear mathematical framework, which allows to define the boundary density matrix induced by a bulk spin network states after tracing out the bulk degrees of freedom. We ask the question of the bulk reconstruction and prove a boundary-to-bulk universal reconstruction procedure, to be understood as a purification of the mixed boundary state into a pure bulk state. We further perform a first investigation in the algebraic structure of induced boundary density matrices and show how correlations between bulk excitations, i.e. quanta of 3d geometry, get reflected into the boundary density matrix.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑