Time and a physical Hamiltonian for quantum gravity

Abstract

We present a non-perturbative quantization of general relativity coupled to dust and other matter fields. The dust provides a natural time variable, leading to a physical Hamiltonian with spatial diffeomorphism symmetry. The surprising feature is that the Hamiltonian is not a square root. This property, together with the kinematical structure of loop quantum gravity, provides a complete theory of quantum gravity, and puts in technical reach applications to cosmology, quantum gravitational collapse and Hawking radiation.

5 pages, version to appear in Phys. Rev. Lett

References in corpus (6)

• Loop Quantum Cosmology: An Overview
• Algebraic Quantum Gravity (AQG) I. Conceptual Setup
• Gravity quantized
• Inhomogeneous Loop Quantum Cosmology: Hybrid Quantization of the Gowdy Model
• Dust reference frame in quantum cosmology
• Dynamical Singularity Resolution in Spherically Symmetric Black Hole Formation

Cited by in corpus (124)

• The Trinity of Relational Quantum Dynamics
• From black holes to white holes: a quantum gravitational, symmetric bounce
• Scalar Material Reference Systems and Loop Quantum Gravity
• Relational Observables in Gravity: a Review
• Positive cosmological constant in loop quantum cosmology
• Black hole collapse and bounce in effective loop quantum gravity
• Quantum gravity of dust collapse: shock waves from black holes
• Equivalence of approaches to relational quantum dynamics in relativistic settings
• On the fate of quantum black holes
• Effective relational dynamics of a nonintegrable cosmological model
• How to switch between relational quantum clocks
• Unitarity, clock dependence and quantum recollapse in quantum cosmology
• Effective Dynamics from Coherent State Path Integral of Full Loop Quantum Gravity
• Can chaos be observed in quantum gravity?
• Hamiltonian operator for loop quantum gravity coupled to a scalar field
• Quantum Reduced Loop Gravity: Semiclassical limit
• A relational Hamiltonian for group field theory
• Cosmological Coherent State Expectation Values in LQG I. Isotropic Kinematics
• A curvature operator for LQG
• Hamiltonian Renormalisation I: Derivation from Osterwalder-Schrader Reconstruction
• Spherical symmetric gravitational collapse of a dust cloud: polymerized dynamics in reduced phase space
• Loop quantum cosmology of a radiation-dominated flat FLRW universe
• Towards a reduced phase space quantization in loop quantum cosmology with an inflationary potential
• Reduced Loop Quantization with four Klein-Gordon Scalar Fields as Reference Matter
• An elementary introduction to loop quantum gravity
• Symmetry and Evolution in Quantum Gravity
• Mukhanov-Sasaki equation in manifestly gauge-invariant linearized cosmological perturbation theory with dust reference fields
• Matrix Elements of Lorentzian Hamiltonian Constraint in LQG
• Status of Birkhoff's theorem in polymerized semiclassical regime of Loop Quantum Gravity
• Time evolution in deparametrized models of loop quantum gravity
• Ground state of the universe and the cosmological constant. A nonperturbative analysis
• Reduced Phase Space Quantization of Black Holes: Path Integrals, and Effective Dynamics
• Loop quantum gravity coupled to a scalar field
• QFT on quantum spacetime: a compatible classical framework
• Hamiltonian Renormalization III. Renormalisation Flow of 1+1 dimensional free scalar fields: Properties
• On the properties of the irrotational dust model
• Inflation from non-minimally coupled scalar field in loop quantum cosmology
• Hamiltonian group field theory with multiple scalar matter fields
• Hamiltonian Renormalisation II. Renormalisation Flow of 1+1 dimensional free scalar fields: Derivation
• General relativity in the radial gauge: Reduced phase space and canonical structure
• Reconstruction of mimetic gravity in a non-singular bouncing universe from quantum gravity
• Limiting curvature mimetic gravity for group field theory condensates
• Observations on interfacing loop quantum gravity with cosmology
• Rainbow Oppenheimer-Snyder collapse and the entanglement entropy production
• The Universe as an Oscillator
• Singularity resolution from polymer quantum matter
• Rainbow Black Hole From Quantum Gravitational Collapse
• A quantum reduction to spherical symmetry in loop quantum gravity
• Separable Hilbert space for loop quantization
• Linearized gravity with matter time
• Observables for General Relativity related to geometry
• Gauge invariant canonical cosmological perturbation theory with geometrical clocks in extended phase space - a review and applications
• Scalar curvature operator for models of loop quantum gravity on a cubical graph
• Dynamical Properties of the Mukhanov-Sasaki Hamiltonian in the context of adiabatic vacua and the Lewis-Riesenfeld invariant
• Closing the gaps in quantum space and time: Conformally augmented gauge structure of gravitation
• Anisotropic loop quantum cosmology with self-dual variables
• Polymer inflation
• Relating dust reference models to conventional systems in manifestly gauge invariant perturbation theory
• Paths to gravitation via the gauging of parameterized field theories
• Classical and quantum cosmology with York time
• Unitary evolution of the quantum universe with a Brown-Kuchar dust
• Loop quantum gravity without the Hamiltonian constraint
• Chaos, Dirac observables and constraint quantization
• Black hole singularity resolution in unimodular gravity from unitarity
• Quantum theory of electromagnetic fields in a cosmological quantum spacetime
• Canonical loop quantization of the lowest-order projectable Horava gravity
• On the relation between reduced quantisation and quantum reduction for spherical symmetry in loop quantum gravity
• Towards anisotropic cosmology in group field theory
• Quantization of time and the big bang via scale-invariant loop gravity
• Hamiltonian formulation of gravity as a spontaneously-broken gauge theory of the Lorentz group
• Midisuperspace foam and the cosmological constant
• Mixmaster dynamics in the dust time gauge
• Towards the fundamental spectrum of the Quantum Yang-Mills Theory
• Cosmological perturbation theory with matter time
• Semiclassical cosmology with polymer matter
• Comparing Quantum Gravity Models: String Theory, Loop Quantum Gravity, and Entanglement gravity versus $SU(\infty )$-QGR
• Matter-Geometry entanglement in quantum cosmology
• The volume operator in loop quantum cosmology
• Rainbow metric from quantum gravity: anisotropic cosmology
• Toward matter dynamics in spin foam quantum gravity
• The algebra of observables in Gaußian normal spacetime coordinates
• Physical Hamiltonian for mimetic gravity
• Cosmic time and reduced phase space of General Relativity
• 3D gravity with dust: classical and quantum theory
• On a partially reduced phase space quantisation of general relativity conformally coupled to a scalar field
• Dynamics in canonical models of loop quantum gravity
• Evolution in totally constrained models: Schrödinger vs. Heisenberg pictures
• Metric emerging to massive modes in quantum cosmological space-times
• Quantum speed limit and stability of coherent states in quantum gravity
• Quantum cosmology of the flat universe via closed real-time path integral
• Wave Function of the Universe from a Matrix Valued First-Order Formalism
• Exact path integrals on half-line in quantum cosmology with a fluid clock and aspects of operator ordering ambiguity
• Radiation-dominated bouncing model with slow contraction and inflation
• Hilbert space formalisms for group field theory
• Quantum dust collapse with cosmological constant and methods for constructing conformal diagrams
• Reconstructing the metric in group field theory
• Incompleteness Theorems for Observables in General Relativity
• Loop quantum gravity of a spherically symmetric scalar field coupled to gravity with a clock
• Shock waves in classical dust collapse
• Geometrical Quantum Time in the $U(1{)}^3$ Model of Euclidean Quantum Gravity
• Quantum Gravity, Hydrodynamics and Emergent Cosmology: A Collection of Perspectives
• Quantization of spherically symmetric loop quantum gravity coupled to a scalar field and a clock: the asymptotic limit
• Quantum fluctuations and semiclassicality in an inflaton-driven evolution
• We have time because we shall never know
• Monte Carlo simulation of cosmologies with dust
• Homogeneous-isotropic sector of loop quantum gravity: new approach
• Realization of Dirac quantization in loop quantum gravity
• Linearized 3D gravity with dust
• Isotropic LQC and LQC--inspired Models with a massless scalar field as Generalised Brans--Dicke theories
• Cosmological perturbation theory with York time
• On the dynamics of single-vertex states in quantum-reduced loop gravity
• Gravitation and cosmology with York time
• Gravitational null rays: Covariant Quantization and the Dressing Time
• Relational Time as a Stochastic Variable in ADM Gravity
• Coherent states for fractional powers of the harmonic oscillator Hamiltonian
• Quantum gravitational collapse as a Dirac particle on the half-line
• A Quantum Informational Approach to the Problem of Time
• A loop quantization of the marginally bound Lemaître-Tolman-Bondi dust model
• Solvable model for quantum gravity
• Problem of time and Hamiltonian reduction in the (2+2) formalism
• Quantum scalar fields interacting with quantum black hole asymptotic regions
• Non-Abelian gauge theories invariant under diffeomorphisms
• A possible connection between quantum mechanics and spacetime
• Solution to the problem of time