The effective dynamics of weak coupling loop quantum gravity

Abstract

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.

References in corpus (29)

• Background Independent Quantum Gravity: A Status Report
• Dust as a Standard of Space and Time in Canonical Quantum Gravity
• Fundamental Structure of Loop Quantum Gravity
• Twisted geometries: A geometric parametrisation of SU(2) phase space
• Polyhedra in loop quantum gravity
• Gauge Field Theory Coherent States (GCS) : I. General Properties
• Gauge Field Theory Coherent States (GCS) : II. Peakedness Properties
• Algebraic Quantum Gravity (AQG) I. Conceptual Setup
• Gravity quantized
• Coherent spin-networks
• Towards the QFT on Curved Spacetime Limit of QGR. I: A General Scheme
• New Variables for Classical and Quantum Gravity in all Dimensions I. Hamiltonian Analysis
• Towards the QFT on Curved Spacetime Limit of QGR. II: A Concrete Implementation
• Algebraic Quantum Gravity (AQG) II. Semiclassical Analysis
• Towards an Anomaly-Free Quantum Dynamics for a Weak Coupling Limit of Euclidean Gravity
• New Variables for Classical and Quantum Gravity in all Dimensions III. Quantum Theory
• Effective Dynamics from Coherent State Path Integral of Full Loop Quantum Gravity
• The G_Newton --> 0 Limit of Euclidean Quantum Gravity
• Coherent intertwiner solution of simplicity constraint in all dimensional loop quantum gravity
• Semiclassical Limit of New Path Integral Formulation from Reduced Phase Space Loop Quantum Gravity
• Coherent State Functional Integral in Loop Quantum Cosmology: Alternative Dynamics
• General geometric operators in all dimensional loop quantum gravity
• Twisted Geometries Coherent States for Loop Quantum Gravity
• Polytopes in all dimensional loop quantum gravity
• Coherent State Functional Integrals in Quantum Cosmology
• Perelomov type coherent states of SO(D + 1) in all dimensional loop quantum gravity
• Superposition type coherent states in all dimensional loop quantum gravity
• Geometric parametrization of $SO(D+1)$ phase space of all dimensional loop quantum gravity
• Exploring the Tomlin-Varadarajan quantum constraints in $U(1{)}^3$ loop quantum gravity: solutions and the Minkowski theorem

Cited by in corpus (4)

• Twisted geometry coherent states in all dimensional loop quantum gravity: I. Construction and Peakedness properties
• Twisted geometry coherent states in all dimensional loop quantum gravity: II. Ehrenfest Property
• On the gauge reduction with respect to simplicity constraint in all dimensional loop quantum gravity
• Geometrical Quantum Time in the $U(1{)}^3$ Model of Euclidean Quantum Gravity