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Hamiltonian operator for loop quantum gravity coupled to a scalar field
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We present the construction of a physical Hamiltonian operator in the deparametrized model of loop quantum gravity coupled to a free scalar field. This construction is based on the use of the recently introduced curvature operator, and on the idea of so-called "special loops". We discuss in detail the regularization procedure and the assignment of the loops, along with the properties of the resulting operator. We compute the action of the squared Hamiltonian operator on spin network states, and close with some comments and outlooks.
Forward citations
Cited by 2 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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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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