A Lattice Physics Approach to Spin-Networks in Loop Quantum Gravity
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911066545455104 |
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| author | MacKay, Noah M. |
| author_facet | MacKay, Noah M. |
| contents | In this study, we model a spin-network in loop quantum gravity as a regular tetrahedral lattice, applying lattice physics techniques to study its structure and vertex dynamics. Using the area eigenvalue, $A\propto 8πl_P^2$, we derive a lattice constant $a = 2.707\,l_P$ and construct a vertex Hamiltonian incorporating a Lennard-Jones potential, zero-point energy, and simple harmonic oscillations. A foliation approach enforces the Wheeler-DeWitt constraint via locally non-zero Hamiltonians that globally cancel. Graviton-like perturbations (treated here as spin-0 bosons) modify the vertex energy spectrum, with variational analysis suggesting twelve coherent excitations per vertex. This model frames flat spacetime as a graviton-rich lattice while enforcing a Brownian-like stochastic picture for the gravitons, and offers a basis for extension into curved quantum geometries. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_14630 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Lattice Physics Approach to Spin-Networks in Loop Quantum Gravity MacKay, Noah M. General Relativity and Quantum Cosmology Other Condensed Matter High Energy Physics - Theory 37C86, 81Q35, 82D03, 83C27 In this study, we model a spin-network in loop quantum gravity as a regular tetrahedral lattice, applying lattice physics techniques to study its structure and vertex dynamics. Using the area eigenvalue, $A\propto 8πl_P^2$, we derive a lattice constant $a = 2.707\,l_P$ and construct a vertex Hamiltonian incorporating a Lennard-Jones potential, zero-point energy, and simple harmonic oscillations. A foliation approach enforces the Wheeler-DeWitt constraint via locally non-zero Hamiltonians that globally cancel. Graviton-like perturbations (treated here as spin-0 bosons) modify the vertex energy spectrum, with variational analysis suggesting twelve coherent excitations per vertex. This model frames flat spacetime as a graviton-rich lattice while enforcing a Brownian-like stochastic picture for the gravitons, and offers a basis for extension into curved quantum geometries. |
| title | A Lattice Physics Approach to Spin-Networks in Loop Quantum Gravity |
| topic | General Relativity and Quantum Cosmology Other Condensed Matter High Energy Physics - Theory 37C86, 81Q35, 82D03, 83C27 |
| url | https://arxiv.org/abs/2507.14630 |