Related papers: Spinning into Quantum Geometry: Dirac and Wheeler-DeWitt Dynamics from Stochastic Helicity

Spinning into Quantum Geometry: Dirac and Wheeler-DeWitt Dynamics from Stochastic Helicity

URL: http://arxiv.org/abs/2510.10836v2
Date: Mon, 03 Nov 2025 07:36:57 GMT
Title: Spinning into Quantum Geometry: Dirac and Wheeler-DeWitt Dynamics from Stochastic Helicity
Authors: Partha Nandi, Partha Ghose, Francesco Petruccione,
Abstract summary: Spin networks in loop quantum gravity provide a kinematical picture of quantum geometry.<n>We propose a framework in which each spin-network edge carries helicity-resolved amplitudes.<n>We show that both quantum evolution and gravitational geometry emerge within a single framework.
Score: 0.13999481573773068
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: 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.

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