论文标题
一阶量子校正在连贯的状态期望值中的一阶量子校正值哈密顿式的概念 - 概述和结果
First-Order Quantum Correction in Coherent State Expectation Value of Loop-Quantum-Gravity Hamiltonian: Overview and Results
论文作者
论文摘要
鉴于循环 - 量子 - 重力（LQG）非改变的汉密尔顿$ \ wideHat {h [n]} $，连贯的状态期望值$ \ langle \ langle \ wideHat {h [n]} \ rangle $承认，$ \ ell^2 _ {在本文中，我们明确地计算$ \ langle \ wideHat {h [n]} \ rangle $在立方图上的$ to $ \ ell^2 _ {\ rm p} $中的线性顺序，当相干状态以均质和同位素的效果数据达到峰值时。在我们的计算中，开发了一种强大的算法来克服计算$ \ langle \ wideHat {h [n]} \ rangle $的复杂性。特别是，我们算法中的一些关键创新大大降低了$ \ langle \ wideHat {h [n]} \ rangle $的洛伦兹部分中的计算复杂性。此外，本工作中开发的算法使得可以在一个边缘上计算任意单位和通量的任意单元的期望值，直到任意顺序为$ \ ell _ {\ rm p}^2 $。
Given the Loop-Quantum-Gravity (LQG) non-graph-changing Hamiltonian $\widehat{H[N]}$, the coherent state expectation value $\langle\widehat{H[N]}\rangle$ admits an semiclassical expansion in $\ell^2_{\rm p}$. In this paper, we compute explicitly the expansion of $\langle\widehat{H[N]}\rangle$ on the cubic graph to the linear order in $\ell^2_{\rm p}$, when the coherent state is peaked at the homogeneous and isotropic data of cosmology. In our computation, a powerful algorithm is developed to overcome the complexity in computing $\langle \widehat{H[N]} \rangle$. In particular, some key innovations in our algorithm substantially reduce the computational complexity in the Lorentzian part of $\langle\widehat{H[N]}\rangle$. Moreover, the algorithm developed in the present work makes it possible to compute the expectation value of arbitrary monomial of holonomies and fluxes on one edge up to arbitrary order of $\ell_{\rm p}^2$.
