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 $\ell_{\rm p}^2$.
Violation of Bell inequality from a squeezed coherent state of inflationary perturbations
Indian Statistical Institute（印度统计研究所）；Indian Association for the Cultivation of Science（印度科学培养协会）；Department of Physics, Indian Institute of Science（印度科学学院物理系）
Coherent quantum geometry: de Sitter spacetime in different foliations
Instituto de Física Teórica, Unesp（圣保罗州立大学理论物理研究所）；Dipartimento di Fisica e Astronomia, Università di Bologna（博洛尼亚大学物理与天文学系）；I.N.F.N., Sezione di Bologna（意大利国家核物理学院博洛尼加分院）；Alma Mater Research Center on Applied Mathematics (AM)（阿爾瑪母特應用數學研究中心）
Bridging Quantum and Semiclassical Volume: A Numerical Study of Coherent State Matrix Elements in Loop Quantum Gravity
School of Physics and Optoelectronics, South China University of Technology（华南理工大学物理与光电工程学院）；Institute for Theoretical Sciences and Department of Physics, Westlake University（西湖大学理论科学研究院和物理系）
