Quantum isotropy and the reduction of dynamics in Bianchi I
Quantum isotropy and the reduction of dynamics in Bianchi I
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DOI：
10.1088/1361-6382/ac337c
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发表时间：
2021-02
影响因子：
3.5
通讯作者：
C. Beetle;J. Engle;M. Hogan;P. Mendonca
中科院分区：
文献类型：
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作者：
C. Beetle;J. Engle;M. Hogan;P. Mendonca
作者之前介绍了环圈量子引力(LQG)均匀各向同性部分的微分同胚不变定义，以及嵌入环圈量子宇宙学(LQC)的程序。对于更简单但在物理上仍然非平凡的情况，本论文详细地编制了该程序，其中嵌入的目标是齐次的但不是各向同性的Bianci I模型。在完全理论中，施加齐性和各向同性的微分同态不变条件简化为施加在已经齐次的比安奇I时空上的各向同性的条件。约化条件在规范修正Bianci模型后仍然允许的剩余微分同态下是不变的。我们证明了量子各向同性模型存在唯一嵌入到齐次量子Biachi模型中，该模型(A)相对于这种剩余微分同胚的作用是协变的，并且(B)缠绕了(带符号)体积算符和至少一个定向哈勃速率。这种嵌入也交织在各自的环路量子宇宙学模型中的所有其他感兴趣的算符，包括它们的哈密顿约束。因此，它在比安奇I模型的各向同性部分的动力学和量子化的各向同性模型之间建立了精确的等价，而不仅仅是它们的运动学。我们还讨论了这里定义的嵌入映射与之前由Ashtekar和Wilson-Ewing定义的投影映射之间的伴随关系。最后，我们强调了某些特征，它们简化了这个简化的嵌入问题，但在将齐次和各向同性LQC嵌入到完全LQG中时，可能没有直接类似的特征。
The authors previously introduced a diffeomorphism-invariant definition of a homogeneous and isotropic sector of loop quantum gravity (LQG), along with a program to embed loop quantum cosmology (LQC) into it. The present paper works out that program in detail for the simpler, but still physically non-trivial, case where the target of the embedding is the homogeneous, but not isotropic, Bianchi I model. The diffeomorphism-invariant conditions imposing homogeneity and isotropy in the full theory reduce to conditions imposing isotropy on an already homogeneous Bianchi I spacetime. The reduced conditions are invariant under the residual diffeomorphisms still allowed after gauge fixing the Bianchi I model. We show that there is a unique embedding of the quantum isotropic model into the homogeneous quantum Bianchi I model that (a) is covariant with respect to the actions of such residual diffeomorphisms, and (b) intertwines both the (signed) volume operator and at least one directional Hubble rate. That embedding also intertwines all other operators of interest in the respective loop quantum cosmological models, including their Hamiltonian constraints. It thus establishes a precise equivalence between dynamics in the isotropic sector of the Bianchi I model and the quantized isotropic model, and not just their kinematics. We also discuss the adjoint relationship between the embedding map defined here and a projection map previously defined by Ashtekar and Wilson-Ewing. Finally, we highlight certain features that simplify this reduced embedding problem, but which may not have direct analogues in the embedding of homogeneous and isotropic LQC into full LQG.