First-order quantum correction in coherent state expectation value of loop-quantum-gravity Hamiltonian - Zhang, Cong; Song, Shicong; Han, Muxin (Physical Review D, 2022)
Given the nongraph-changing Hamiltonian H[N]^ in loop quantum gravity (LQG), H[N], the coherent state expectation value of H[N], admits a semiclassical expansion in ℓp2. In this paper, we explicitly compute the expansion of H[N] to the linear order in ℓp2 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, supported by rigorous proofs and several theorems, is developed to overcome the complexity in the computation of H[N]^. Particularly, some key innovations in our algorithm substantially reduce the complexity in computing the Lorentzian part of H[N]^. Moreover, with the algorithm developed in the present work, we can compute the expectation value of arbitrary monomial of holonomies and fluxes on one edge up to arbitrary order of ℓp2. Finally, some quantum correction effects resulted from H[N]^ in cosmology are discussed at the end of this paper.
CRIS-Team Scopus Importer:2022-03-25