Effective dynamics from coherent state path integral of full loop quantum gravity
Effective dynamics from coherent state path integral of full loop quantum gravity
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DOI：
10.1103/physrevd.101.046003
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发表时间：
2019-10
影响因子：
5
通讯作者：
Muxin Han;Hongguang Liu
中科院分区：
文献类型：
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作者：
Muxin Han;Hongguang Liu
从有效动力学的角度出发，提出了一种将圈量子宇宙学（LQC）与圈量子引力（LQG）联系起来的新方法。我们从全正则LQG的第一性原理出发，导出了大爆炸奇异性分解和大反弹。我们的结果是在LQG的约简相空间量子化的框架下得到的。作为我们工作的关键一步，我们利用相干态导出了一个新的由物理哈密顿量产生的跃迁振幅的离散路径积分公式。路径积分公式的半经典近似给出了一组有趣的有效运动方程（EOM）的完整LQG。当求解具有均匀各向同性各向异性的EOM时，我们在μ0格式中再现了LQC有效动力学。这个解用大反弹代替了大爆炸奇点。最后，我们讨论了有效动力学的μ ′-格式与路径积分公式的连续极限之间的可能联系。
A new routine is proposed to relate loop quantum cosmology (LQC) to loop quantum gravity (LQG) from the perspective of effective dynamics. We derive the big-bang singularity resolution and big bounce from the first principle of full canonical LQG. Our results are obtained in the framework of the reduced phase space quantization of LQG. As a key step in our work, we derive with coherent states a new discrete path integral formula of the transition amplitude generated by the physical Hamiltonian. The semiclassical approximation of the path integral formula gives an interesting set of effective equations of motion (EOMs) for full LQG. When solving the EOMs with homogeneous and isotropic ansatz, we reproduce the LQC effective dynamics in the μ0-scheme. The solution replaces the big-bang singularity by a big bounce. In the end, we comment on the possible relation between the μ¯-scheme of effective dynamics and the continuum limit of the path integral formula.