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Lattice Quantum Gravity from Stochastic 3-Geometries

N. Nakazawa
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Abstract

I propose the Langevin equation for 3-geometries in the Ashtekar's formalism to describe 4D Euclidean quantum gravity, in the sense that the corresponding Fokker-Planck hamiltonian recovers the hamiltonian in 4D quantum gravity exactly. The stochastic time corresponds to the Euclidean time in the gauge, N=1 and $N^i=0$. In this approach, the time evolution in 4D quantum gravity is understood as a stochastic process where the quantum fluctuation of ` ` triad \rq\rq is characterized by the curvature at the one unit time step before. The lattice regularization of 4D quantum gravity is presented in this context.

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N. Nakazawa. 1995-09-18. Lattice Quantum Gravity from Stochastic 3-Geometries. https://arxiv.org/abs/gr-qc/9508045

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