Gauge-invariant coherent states for Loop Quantum Gravity I: Abelian gauge groups
arXiv:0709.4619 · doi:10.1088/0264-9381/26/4/045011
Abstract
In this paper we investigate the properties of gauge-invariant coherent states for Loop Quantum Gravity, for the gauge group U(1). This is done by projecting the corresponding complexifier coherent states, which have been applied in numerous occasions to investigate the semiclassical limit of the kinematical sector, to the gauge-invariant Hilbert space. This being the first step to construct physical coherent states, we arrive at a set of gauge-invariant states that approximate well the gauge-invariant degrees of freedom of abelian LQG. Furthermore, these states turn out to encode explicit information about the graph topology, and show the same pleasant peakedness properties known from the gauge-variant complexifier coherent states.
36 pages
References in corpus (25)
- Quantum Spin Dynamics (QSD)
- Loop Quantum Gravity
- Spin Networks and Quantum Gravity
- Quantization of diffeomorphism invariant theories of connections with local degrees of freedom
- A new spinfoam vertex for quantum gravity
- Uniqueness of diffeomorphism invariant states on holonomy-flux algebras
- The Phoenix Project: Master Constraint Programme for Loop Quantum Gravity
- Gauge Field Theory Coherent States (GCS) : I. General Properties
- Gauge Field Theory Coherent States (GCS) : II. Peakedness Properties
- Semiclassical Approximations in Phase Space with Coherent States
- QSD III : Quantum Constraint Algebra and Physical Scalar Product in Quantum General Relativity
- Algebraic Quantum Gravity (AQG) I. Conceptual Setup
- An invitation to loop quantum gravity
- Gauge Field Theory Coherent States (GCS) : III. Ehrenfest Theorems
- Asymptotics of Relativistic Spin Networks
- Coherent states for a quantum particle on a circle
- Quantization of the canonically conjugate pair angle and orbital angular momentum
- Towards the QFT on Curved Spacetime Limit of QGR. I: A General Scheme
- Towards the QFT on Curved Spacetime Limit of QGR. II: A Concrete Implementation
- Asymptotics of 10j symbols
- Algebraic Quantum Gravity (AQG) II. Semiclassical Analysis
- Gauge-invariant coherent states for Loop Quantum Gravity I: Abelian gauge groups
- Algebraic Quantum Gravity (AQG) III. Semiclassical Perturbation Theory
- Loop quantum gravity and quanta of space: a primer
- The graviton vacuum as a distributional state in kinematic Loop Quantum Gravity
Cited by in corpus (43)
- The Spin Foam Approach to Quantum Gravity
- A Short Review of Loop Quantum Gravity
- Twisted geometries: A geometric parametrisation of SU(2) phase space
- Polyhedra in loop quantum gravity
- Towards Spinfoam Cosmology
- Algebraic Quantum Gravity (AQG) IV. Reduced Phase Space Quantisation of Loop Quantum Gravity
- Coherent spin-networks
- Quantum geometry from phase space reduction
- Gauge-invariant coherent states for Loop Quantum Gravity I: Abelian gauge groups
- Perspectives on the dynamics in a loop quantum gravity effective description of black hole interiors
- Gauge-invariant coherent states for Loop Quantum Gravity II: Non-abelian gauge groups
- Towards classical geometrodynamics from Group Field Theory hydrodynamics
- Quantum Gravity: A Brief History of Ideas and Some Prospects
- Spinfoams in the holomorphic representation
- Loop Quantum Gravity Vacuum with Nondegenerate Geometry
- Cosmological Coherent State Expectation Values in LQG I. Isotropic Kinematics
- Loop Quantum Gravity
- Quasi-local holographic dualities in non-perturbative 3d quantum gravity II - From coherent quantum boundaries to BMS3 characters
- From Classical To Quantum Gravity: Introduction to Loop Quantum Gravity
- Semiclassical analysis of the Loop Quantum Gravity volume operator: I. Flux Coherent States
- Loop expansion and the bosonic representation of loop quantum gravity
- Learning about Quantum Gravity with a Couple of Nodes
- Group Field Theory and Holographic Tensor Networks: Dynamical Corrections to the Ryu-Takayanagi formula
- Holonomy Spin Foam Models: Boundary Hilbert spaces and Time Evolution Operators
- Spinors and Twistors in Loop Gravity and Spin Foams
- Emergent Braided Matter of Quantum Geometry
- Intersecting Quantum Gravity with Noncommutative Geometry - a Review
- C*-algebras of Holonomy-Diffeomorphisms & Quantum Gravity I
- Quantum Gravity coupled to Matter via Noncommutative Geometry
- Conserved Topological Defects in Non-Embedded Graphs in Quantum Gravity
- Coherent State Operators in Loop Quantum Gravity
- Algorithmic approach to Cosmological Coherent State Expectation Values in LQG
- On a Derivation of the Dirac Hamiltonian From a Construction of Quantum Gravity
- Quantum Holonomy Theory
- Introduction to SU(2) recoupling theory and graphical methods for loop quantum gravity
- Dynamics in canonical models of loop quantum gravity
- Spin foam propagator: A new perspective to include a cosmological constant
- Lattice Loop Quantum Gravity
- Coherent states for compact Lie groups and their large-N limits
- Energy spectrum of black holes : a new view
- Loop quantum gravity with optimal control path integral, and application to black hole tunneling
- Non-Ultralocality and Causality in the Relational Framework of Canonical Quantum Gravity
- Nonlocal correlations for semiclassical states in loop quantum gravity