Dynamically Triangulating Lorentzian Quantum Gravity

Details Dynamically Triangulating Lorentzian Quantum Gravity Dynamically Triangulating Lorentzian Quantum Gravity

2001-05-27

arxiv.org/abs/hep-th/0105267v1

Nucl.Phys. B610 (2001) 347-382

Physics

High Energy Physics

High Energy Physics - Theory

41 pages, 14 figures

Scientific paper

10.1016/S0550-3213(01)00297-8

Fruitful ideas on how to quantize gravity are few and far between. In this paper, we give a complete description of a recently introduced non-perturbative gravitational path integral whose continuum limit has already been investigated extensively in d less than 4, with promising results. It is based on a simplicial regularization of Lorentzian space-times and, most importantly, possesses a well-defined, non-perturbative Wick rotation. We present a detailed analysis of the geometric and mathematical properties of the discretized model in d=3,4. This includes a derivation of Lorentzian simplicial manifold constraints, the gravitational actions and their Wick rotation. We define a transfer matrix for the system and show that it leads to a well-defined self-adjoint Hamiltonian. In view of numerical simulations, we also suggest sets of Lorentzian Monte Carlo moves. We demonstrate that certain pathological phases found previously in Euclidean models of dynamical triangulations cannot be realized in the Lorentzian case.

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