2021/02/28 by Cong Zhang, Shicong Song, Muxin Han · 1 citation
Mathematics · Physics and Astronomy · #Algorithm #Black Holes and Theoretical Physics #Combinatorics #Computation #Cosmology and Gravitation Theories #Discrete mathematics #Graph #Hamiltonian (control theory) #Hamiltonian path #Loop quantum gravity #Mathematical optimization #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum computer #Quantum gravity #Quantum mechanics #Semiclassical physics #astro-ph.CO #gr-qc #hep-lat #hep-th
paper · pdf · doi:10.1103/physrevd.105.064008
published as Phys. Rev. D 105, 064008 (2022) · 29+25 pages, 2 figures, presenting the detailed derivations of our previous work arXiv:2012.14242, adapted to the published version
openalex publication_date 2022/03/07 · arxiv created 2022/03/10 · arxiv updated 2022/03/14 · openalex created_date 2022/04/03 · openalex updated_date 2026/08/06
Given the non-graph-changing Hamiltonian \widehatH[N] in Loop Quantum Gravity (LQG), ⟨\widehatH[N]⟩, the coherent state expectation value of \widehatH[N], admits an semiclassical expansion in ℓ2\rm p. In this paper, as presenting the detailed derivations of our previous work arXiv:2012.14242, we explicitly compute the expansion of ⟨\widehatH[N]⟩ to the linear order in ℓ2\rm p on the cubic graph with respect to the coherent state peaked at the homogeneous and isotropic data of cosmology. In our computation, a powerful algorithm is developed, supported by rigorous proofs and several theorems, to overcome the complexity in the computation of ⟨ \widehatH[N] ⟩. Particularly, some key innovations in our algorithm substantially reduce the complexity in computing the Lorentzian part of ⟨\widehatH[N]⟩. Additionally, some quantum correction effects resulting from ⟨\widehatH[N]⟩ in cosmology are discussed at the end of this paper.