Effective dynamics from coherent state path integral of full loop quantum gravity

2019/10/31 by Muxin Han, Hongguang Liu · 3 citations
Mathematics · Physics and Astronomy · #Ansatz #Big Bounce #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Linear-quadratic-Gaussian control #Loop quantum cosmology #Loop quantum gravity #Mathematical analysis #Mathematical optimization #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Optimal control #Path integral formulation #Physics #Quantum #Quantum cosmology #Quantum gravity #Quantum mechanics #Semiclassical physics #Singularity #gr-qc #hep-th

paper · pdf · doi:10.1103/physrevd.101.046003

published as Phys. Rev. D 101, 046003 (2020) · 30+10 pages, 2 figures

openalex created_date 2019/10/18 · arxiv created 2019/12/23 · openalex publication_date 2020/02/05 · arxiv updated 2020/02/12 · openalex updated_date 2026/08/06

Abstract

A new routine is proposed to relate loop quantum cosmology (LQC) to loop quantum gravity (LQG) from the perspective of effective dynamics. We derive the big-bang singularity resolution and big bounce from the first principle of full canonical 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 equations of motion (EOMs) for full LQG. When solving the EOMs with homogeneous and isotropic ansatz, we reproduce the LQC effective dynamics in the \ensuremathμ₀-scheme. The solution replaces the big-bang singularity by a big bounce. In the end, we comment on the possible relation between the \ensuremathμ-scheme of effective dynamics and the continuum limit of the path integral formula.

Citations

• Quantum spin dynamics
• New scalar constraint operator for loop quantum gravity
• New length operator for loop quantum gravity
• Coherent states for canonical quantum general relativity and the infinite tensor product extension
• General relativity without coordinates
• Manifestly gauge-invariant general relativistic perturbation theory: II. FRW background and first order
• Quantum Nature of the Big Bang
• Gravity quantized: Loop quantum gravity with a scalar field
• On the relation between operator constraint, master constraint, reduced phase space and path integral quantization
• Loop Quantum Cosmology
• Algebraic quantum gravity (AQG): III. Semiclassical perturbation theory
• Quantization of diffeomorphism invariant theories of connections with local degrees of freedom
• Improved regularization from Quantum Reduced Loop Gravity
• Loop Quantum Cosmology: A brief review
• Planck stars

Cited by

• Manifestly Gauge-Invariant Cosmological Perturbation Theory from Full Loop Quantum Gravity
• Semiclassical Limit of New Path Integral Formulation from Reduced Phase Space Loop Quantum Gravity
• First-Order Quantum Correction in Coherent State Expectation Value of Loop-Quantum-Gravity Hamiltonian