Relating spin-foam to canonical loop quantum gravity by graphical calculus
arXiv:2102.05881 · doi:10.1103/PhysRevD.104.044025
Abstract
The graphical calculus method is generalized to study the relation between covariant and canonical dynamics of loop quantum gravity. On one hand, a graphical derivation of the partition function of the generalized Euclidean Engle-Pereira-Rovelli-Livine (EPRL) spin-foam model is presented. On the other hand, the action of a Euclidean Hamiltonian constraint operator on certain spin network states is calculated by graphical method. It turns out that the EPRL model can provide a rigging map such that the Hamiltonian constraint operator is weakly satisfied on certain physical states for the Immirzi parameter . In this sense, the quantum dynamics between the covariant and canonical formulations are consistent to each other.
arXiv comment19 pages
References in corpus (38)
- 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)
- The Spin Foam Approach to Quantum Gravity
- LQG vertex with finite Immirzi parameter
- QSD V : Quantum Gravity as the Natural Regulator of Matter Quantum Field Theories
- Relativistic spin networks and quantum gravity
- A new spinfoam vertex for quantum gravity
- Projective Techniques and Functional Integration
- A New Spin Foam Model for 4d Gravity
- Representations of the holonomy algebras of gravity and non-Abelian gauge theories
- Uniqueness of diffeomorphism invariant states on holonomy-flux algebras
- Fundamental Structure of Loop Quantum Gravity
- Quantum Gravity and Regge Calculus
- A Lorentzian Signature Model for Quantum General Relativity
- Lectures on Loop Quantum Gravity
- A length operator for canonical quantum gravity
- Spin-Foams for All Loop Quantum Gravity
- Towards an Anomaly-Free Quantum Dynamics for a Weak Coupling Limit of Euclidean Gravity
- New length operator for loop quantum gravity
- Linking covariant and canonical LQG: new solutions to the Euclidean Scalar Constraint
- Generalized Spinfoams
- Hamiltonian operator for loop quantum gravity coupled to a scalar field
- Linking covariant and canonical LQG II: Spin foam projector
- New Hamiltonian constraint operator for loop quantum gravity
- From Classical To Quantum Gravity: Introduction to Loop Quantum Gravity
- Coherent states, constraint classes, and area operators in the new spin-foam models
- Towards an Anomaly-Free Quantum Dynamics for a Weak Coupling Limit of Euclidean Gravity: Diffeomorphism Covariance
- Bouncing evolution in a model of loop quantum gravity
- Quantum spin dynamics
- The constraint algebra in Smolins' limit of 4d Euclidean Gravity
- New volume and inverse volume operators for loop quantum gravity
- The volume operator in covariant quantum gravity
- Towards the self-adjointness of a Hamiltonian operator in loop quantum gravity
- On quantum propagation in Smolin's weak coupling limit of 4d Euclidean Gravity
- Consistency check on the fundamental and alternative flux operators in loop quantum gravity