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Time and a physical Hamiltonian for quantum gravity
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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.
Forward citations
Cited by 9 Pith papers
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Prism Effect in Quantum Gravity
Extended Born-Oppenheimer coupling of the EM field to quantum geometry yields chromatic dispersion of light—a prism effect proposed as an all-energy quantum-gravity probe on a quantum FLRW background.
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Relational Observables in Group Field Theory
POVM-based conditioning on scalar-field quantum reference frames defines relational observables in group field theory that match prior number and volume results on coherent states.
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Integral Hilbert spaces and the dynamics of loop quantum cosmos
In a loop quantum cosmology model with negative cosmological constant, semiclassical states built by integrating over all superselection sectors behave no differently from single-sector states, with differences below ...
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On the dynamics of single-vertex states in quantum-reduced loop gravity
The Hamiltonian of single-vertex states in quantum-reduced loop gravity formally matches Bianchi I loop quantum cosmology, and an analogy suggests adding a non-trivial Lorentzian curvature term to the cosmology Hamiltonian.
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Dust collapse and bounce in spherically symmetric quantum-inspired gravity models
Algebraic equations from Hamiltonian constraints on vacuum spherically symmetric metrics describe non-homogeneous dust collapse and bounce, applied to quantum-inspired models to recover or find new bounce results.
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Canonical form of a deformed Poisson bracket spacetime
A Hamiltonian is constructed that renders a deformed Poisson bracket spacetime theory canonical and covariant, enabling consistent coupling to scalar matter and dust.
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Polymer Bianchi-I with polymer matter
In a Bianchi-I universe with polymer quantization of both geometry and a massless scalar, the matter polymer scale shifts the quantum bounce and alters volume and anisotropy evolution.
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Polymer cosmology with polymer matter: Effective dynamics
A polymer-quantized scalar field on a polymer-quantized FLRW background produces a bounce whose location depends on the matter polymer scale, with generic asymmetric evolution across the bounce.
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Quantum-reduced loop gravity: New perspectives on the kinematics and dynamics
The paper reformulates quantum-reduced loop gravity with a master constraint operator and finds that its single-node Hamiltonian matches the Bianchi I loop quantum cosmology Hamiltonian.
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