Emergent symmetries in the canonical tensor model
Emergent symmetries in the canonical tensor model
复制标题
正则张量模型中的涌现对称性
DOI：
10.1093/ptep/pty038
复制
发表时间：
2018
影响因子：
3.5
通讯作者：
Sasakura Naoki
中科院分区：
文献类型：
--
作者：
Obster Dennis;Sasakura Naoki
正则张量模型（英语：Canonical tensor model，CTM）是一个张量模型，提出了一个经典和量子力学一致的引力描述，被表述为一个第一类约束系统，与广义相对论的ADM形式主义具有结构相似性。经典CTM产生了一个形式连续极限的广义相对论系统，它的出现应该由量子CTM来解释。在本文中，我们研究的对称性波函数，正是解决了量子约束的CTM。我们已经发现，它有很强的峰值在一些李群下不变的配置，如我们以前的论文中描述的机制所预测的。一个令人惊讶的结果是，不仅在具有正定签名的李群下，而且在具有洛伦兹签名的李群下，配置不变的偏好。这样的对称性可以描述时空的全球结构，我们的结果是令人鼓舞的显示时空出现在CTM。为了验证波函数的渐近收敛性，我们还分析了渐近行为，这在很大程度上似乎是控制。
The canonical tensor model (CTM) is a tensor model proposing a classically and quantum mechanically consistent description of gravity, formulated as a first-class constraint system with structural similarities to the ADM formalism of general relativity. The classical CTM produces a general relativistic system in a formal continuum limit, the emergence of which should be explained by the quantum CTM. In this paper we study the symmetry properties of a wave function that exactly solves the quantum constraints of the CTM. We have found that it has strong peaks at configurations invariant under some Lie groups, as predicted by a mechanism described in our previous paper. A surprising result is the preference for configurations invariant not only under Lie groups with positive definite signature, but also with Lorentzian signature. Such symmetries could characterize the global structures of spacetimes, and our results are encouraging towards showing spacetime emergence in the CTM. To verify the asymptotic convergence of the wave function we have also analyzed the asymptotic behavior, which for the most part seems to be well under control.