First-Order Quantum Correction in Coherent State Expectation Value of Loop-Quantum-Gravity Hamiltonian: Overview and Results

2020/12/28 by Zhang, Cong, Song, Shicong, Han, Muxin · 1 citation
#Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2012.14242

Abstract

Given the Loop-Quantum-Gravity (LQG) non-graph-changing Hamiltonian \widehatH[N], the coherent state expectation value ⟨\widehatH[N]⟩ admits an semiclassical expansion in ℓ²_{\rm p}. In this paper, we compute explicitly the expansion of ⟨\widehatH[N]⟩ on the cubic graph to the linear order in ℓ²_{\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 ⟨ \widehatH[N] ⟩. In particular, some key innovations in our algorithm substantially reduce the computational complexity in the Lorentzian part of ⟨\widehatH[N]⟩. 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 ℓ_{\rm p}².

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• First-Order Quantum Correction in Coherent State Expectation Value of Loop-Quantum-Gravity Hamiltonian

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