Spinning into Quantum Geometry: Dirac and Wheeler-DeWitt Dynamics from Stochastic Helicity
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| Format: | Preprint |
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2025
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| _version_ | 1866909881552863232 |
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| author | Nandi, Partha Ghose, Partha Petruccione, Francesco |
| author_facet | Nandi, Partha Ghose, Partha Petruccione, Francesco |
| contents | Spin networks in loop quantum gravity provide a kinematical picture of quantum geometry but lack a natural mechanism for dynamical Dirac-type evolution, while the Wheeler--DeWitt equation typically enters only as an imposed constraint. We propose a stochastic framework in which each spin-network edge carries helicity-resolved amplitudes -- two-state internal labels that undergo Poisson-driven flips. The resulting coupled master equations, after analytic continuation and the introduction of a fundamental length scale, generate Dirac-type dynamics on discrete geometry. At long times, the same process relaxes to helicity-symmetric equilibrium states, which are shown to satisfy a Wheeler--DeWitt-type condition. In this way, both quantum evolution and the gravitational constraint emerge within a single probabilistic framework. Our approach thus provides a background-independent and stochastic route to quantum geometry, offering an alternative to canonical quantization and a fresh perspective on the problem of time. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_10836 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spinning into Quantum Geometry: Dirac and Wheeler-DeWitt Dynamics from Stochastic Helicity Nandi, Partha Ghose, Partha Petruccione, Francesco General Relativity and Quantum Cosmology High Energy Physics - Theory Quantum Physics Spin networks in loop quantum gravity provide a kinematical picture of quantum geometry but lack a natural mechanism for dynamical Dirac-type evolution, while the Wheeler--DeWitt equation typically enters only as an imposed constraint. We propose a stochastic framework in which each spin-network edge carries helicity-resolved amplitudes -- two-state internal labels that undergo Poisson-driven flips. The resulting coupled master equations, after analytic continuation and the introduction of a fundamental length scale, generate Dirac-type dynamics on discrete geometry. At long times, the same process relaxes to helicity-symmetric equilibrium states, which are shown to satisfy a Wheeler--DeWitt-type condition. In this way, both quantum evolution and the gravitational constraint emerge within a single probabilistic framework. Our approach thus provides a background-independent and stochastic route to quantum geometry, offering an alternative to canonical quantization and a fresh perspective on the problem of time. |
| title | Spinning into Quantum Geometry: Dirac and Wheeler-DeWitt Dynamics from Stochastic Helicity |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2510.10836 |