2021/11/23 by Gaoping Long, Yongge Ma
Mathematics · Medicine · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Coupling constant #Gravitation #Hamiltonian (control theory) #Holonomy #Loop quantum cosmology #Loop quantum gravity #Mathematical physics #Mathematics #Neuroblastoma Research and Treatments #Noncommutative and Quantum Gravity Theories #Operator (biology) #Path integral formulation #Physics #Quantum #Quantum gravity #Quantum mechanics #Spin foam #gr-qc
paper · pdf · doi:10.1103/physrevd.105.044043
arxiv created 2021/11/23 · openalex publication_date 2022/02/22 · arxiv updated 2022/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
By taking the limit that Newton's Gravitational constant tends to zero, the weak coupling loop quantum gravity can be formulated as a U(1)3 gauge theory instead of the original SU(2) gauge theory. In this paper, a parametrization of the SU(2) holonomy-flux variables by the U(1)3 holonomy-flux variables is introduced, and the Hamiltonian operator based on this parametrization is obtained for the weak coupling loop quantum gravity. It is shown that the effective dynamics obtained from the coherent state path integrals in U(1)3 and SU(2) loop quantum gravity respectively are consistent to each other in the weak coupling limit, provided that the expectation values of the Hamiltonian operators on the coherent states in these two theories coincide with their classical expressions respectively.