Euclidean LQG Dynamics: An Electric Shift in Perspective

Abstract

Loop Quantum Gravity (LQG) is a non-perturbative attempt at quantization of a classical phase space description of gravity in terms of $SU(2)$ connections and electric fields. As emphasized recently [1], on this phase space, classical gravitational evolution in $time$ can be understood in terms of certain gauge covariant generalizations of Lie derivatives with respect to a $spatial$ $SU(2)$ Lie algebra valued vector field called the Electric Shift. We present a derivation of a quantum dynamics for Euclidean LQG which is informed by this understanding. In addition to the physically motivated nature of the action of the Euclidean Hamiltonian constraint so derived, the derivation implies that the spin labels of regulating holonomies are determined by corresponding labels of the spin network state being acted upon thus eliminating the `spin $j$-ambiguity' pointed out by Perez. By virtue of Thiemann's seminal work, the Euclidean quantum dynamics plays a crucial role in the construction of the Lorentzian quantum dynamics so that our considerations also have application to Lorentzian LQG.

arXiv comment37 pages, 7 figures

References in corpus (27)

• Background Independent Quantum Gravity: A Status Report
• Discreteness of area and volume in quantum gravity
• Quantum Theory of Gravity I: Area Operators
• Real Ashtekar Variables for Lorentzian Signature Space-times
• Quantum Spin Dynamics (QSD)
• Spin Networks and Quantum Gravity
• Real and complex connections for canonical gravity
• Uniqueness of diffeomorphism invariant states on holonomy-flux algebras
• The Phoenix Project: Master Constraint Programme for Loop Quantum Gravity
• QSD III : Quantum Constraint Algebra and Physical Scalar Product in Quantum General Relativity
• On the regularization ambiguities in loop quantum gravity
• The length operator in Loop Quantum Gravity
• On the consistency of the constraint algebra in spin network quantum gravity
• Loop constraints: A habitat and their algebra
• Towards an Anomaly-Free Quantum Dynamics for a Weak Coupling Limit of Euclidean Gravity
• Separable Hilbert space in Loop Quantum Gravity
• New scalar constraint operator for loop quantum gravity
• The G_Newton --> 0 Limit of Euclidean Quantum Gravity
• Constraint algebra in LQG reloaded : Toy model of an Abelian gauge theory - II Spatial Diffeomorphisms
• A symmetric scalar constraint for loop quantum gravity
• The Hamiltonian constraint in Polymer Parametrized Field Theory
• The Diffeomorphism Constraint Operator in Loop Quantum Gravity
• Towards an Anomaly-Free Quantum Dynamics for a Weak Coupling Limit of Euclidean Gravity: Diffeomorphism Covariance
• The constraint algebra in Smolins' $G\to 0$ limit of 4d Euclidean Gravity
• Propagation in Polymer Parameterised Field Theory
• On quantum propagation in Smolin's weak coupling limit of 4d Euclidean Gravity
• Exploring the Tomlin-Varadarajan quantum constraints in $U(1{)}^3$ loop quantum gravity: solutions and the Minkowski theorem

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• Master constraint approach to quantum-reduced loop gravity
• Geometrical Quantum Time in the $U(1{)}^3$ Model of Euclidean Quantum Gravity