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

Abstract

Given the non-graph-changing Hamiltonian H[N ] in Loop Quantum Gravity (LQG), H[N ] , the coherent state expectation value of H[N ], admits an semiclassical expansion in 2 p . In this paper, as presenting the detailed derivations of our previous work [1], we explicitly compute the expansion of H[N ] to the linear order in 2 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 H[N ] . Particularly, some key innovations in our algorithm substantially reduce the complexity in computing the Lorentzian part of H[N ] . Additionally, some quantum correction effects resulted from H[N ] in cosmology are discussed at the end of this paper.

Fermion coupling to loop quantum gravity: canonical formulation

“…The spectra of these operators take discrete values, which implies the fundamental discreteness of the spacetime. The purely gravitational Hamiltonian constraint is regularized and promoted to an operator in the kinematic Hilbert space by [25,26,[37][38][39][40][41][42][43][44][45]. The Hamiltonian constraint comprises of the curvature of the connection A.…”