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New Hamiltonian constraint operator for loop quantum gravity
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A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the advantage of the original regularization method, so that its regulated version in the kinematical Hilbert space is diffeomorphism covariant and creates new vertices to the spin networks. The quantum algebra of this Hamiltonian is anomaly-free on shell, and there is less ambiguity in its construction in comparison with the original method. The regularization procedure for this Hamiltonian constraint operator can also be applied to the symmetric model of loop quantum cosmology, which leads to a new quantum dynamics of the cosmological model.
Forward citations
Cited by 4 Pith papers
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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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Inflation in unimodular loop quantum cosmology
In unimodular loop quantum cosmology, an α-attractor potential allows a potential-energy-dominated bounce at the Planck scale that is consistent with CMB observations and may show quantum-gravity imprints.
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Effective dynamics of a homogeneous and isotropic universe with quantum curvature
A new LQC model with an added curvature term produces a quantum bounce that resolves the singularity at lower volume than standard LQC while preserving symmetric effective dynamics.
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Geometrical Quantum Time in the $U(1)^3$ Model of Euclidean Quantum Gravity
In the U(1)^3 toy model of loop quantum gravity, the authors rearrange the quantum Hamiltonian constraint into a discrete evolution equation and, via a questionable continuum limit, a Schrödinger-like equation with a ...
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