Year: 2025
Type: article
Abstract: In this article we examine a Hamiltonian constraint operator governing the dynamics of simple quantum states, whose graph consists of a single six-valent vertex, in quantum-reduced loop gravity. To this end, we first derive the action of the Hamiltonian constraint on generic basis states in the Hilbert space of quantum-reduced loop gravity. Specializing to the example of the single-vertex states, we find that the Euclidean part of the Hamiltonian bears a close formal similarity to the Hamiltonian constraint of Bianchi I models in loop quantum cosmology. Extending the formal analogy to the Lorentzian part of the Hamiltonian suggests a possible modified definition of the Hamiltonian constraint for loop quantum cosmology, in which the Lorentzian part, corresponding to the scalar curvature of the spatial surfaces, is not assumed to be identically vanishing, and is represented by a non-trivial operator in the quantum theory.
Source: Classical and Quantum Gravity
Author: Ilkka Mäkinen
Institution: National Centre for Nuclear Research
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,325
Award: G6184735711
OpenAlex ID: W4409490325