Dynamically Triangulating Lorentzian Quantum Gravity
By J. Ambjørn, J. Jurkiewicz, R. Loll. 2001
303 citations recorded by the source corpus.
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 < 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.
Subfields: Astronomy and Astrophysics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/22b5202f01ca11fcf31fc3f339775c4624483190
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Citations in the corpus
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- Emergent Friedmann dynamics with a quantum bounce from quantum gravity condensates (2016, methodology): “This is also the case for group field theories (GFTs) [8], which can be seen on the one hand as a second quantised formulation of (the kinematics and dynamics of) LQG degrees of freedom [9], although organised in a different Fock-type Hilbert space, and on the other hand as an enrichment of lattice ”
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- The asymptotic safety scenario in quantum gravity: an introduction (2006, methodology): “ality constraint in the definition of the (formal Euclidean) functional integral originally proposed by Teitelboim [142, 143], and recently put to good use in the framework of dynamical triangulations [4]. Just as the inclusion of a good causality constraint is justified retroactively, so would be the”
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