Hamiltonian Constraint in 4D Lattice Quantum Gravity

Astronomy and Astrophysics – Astrophysics

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Scientific paper

We apply stochastic quantization method to realize the hamiltonian constraint for 4D lattice quantum gravity in Ashtekar's canonical formalism. The basic Langevin equation is proposed to reproduce the hamiltonian constraint in the corresponding Fokker-Planck hamiltonian of the stochastic process. The Langevin equation, which is defined in terms of the Ito stochastic calculus by using the white noise, gives a non-perturbative method to construct solutions of the lattice regularized hamiltonian contraint. We discuss the continuum limit of some observables, such as the geodesic distance, by the Schwinger-Dyson equations derived from the basic Langevin equation.

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