Theory Special Seminar: HongGuang Liu (Pengcheng)

title ： Effective Dynamics from Coherent State Path Integral of Full Loop Quantum Gravity

abstract:  

A hot topic of research in Loop Quantum Gravity (LQG) is how to derive effective equations of motion (EOMs) from the theory. In this talk a new routine is proposed to derive the effective dynamics from LQG. Our results are obtained in the framework of the reduced phase space quantization of LQG. As a key step in our work, we derive with coherent states a new discrete path integral formula of the transition amplitude generated by the physical Hamiltonian. The semiclassical approximation of the path integral formula gives an interesting set of effective EOMs for full LQG. When solving the EOMs with homogeneous and isotropic ansatz, we reproduce the Loop Quantum Cosmology (LQC) effective dynamics in mu-0 scheme. The solution replaces the big-bang singularity by a big bounce. The technique is naturally related to numerical relativity since it provides a set of dynamical evolution equations with natural discretization by LQG.  The idea may also be applicable in other theories of interests like topological field theories.