Simplicial Euclidean and Lorentzian Quantum Gravity

@article{Ambjorn2002SimplicialEA,
  title={Simplicial Euclidean and Lorentzian Quantum Gravity},
  author={Jan Ambjorn},
  journal={arXiv: General Relativity and Quantum Cosmology},
  year={2002}
}
  • J. Ambjorn
  • Published 9 January 2002
  • Mathematics
  • arXiv: General Relativity and Quantum Cosmology
One can try to define the theory of quantum gravity as the sum over geometries. In two dimensions the sum over {\it Euclidean} geometries can be performed constructively by the method of {\it dynamical triangulations}. One can define a {\it proper-time} propagator. This propagator can be used to calculate generalized Hartle-Hawking amplitudes and it can be used to understand the the fractal structure of {\it quantum geometry}. In higher dimensions the philosophy of defining the quantum theory… 

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References

SHOWING 1-10 OF 68 REFERENCES
Non-perturbative 3d Lorentzian quantum gravity
TLDR
The phase structure of the Wick-rotated path integral in three dimensions with the aid of computer simulations is investigated, finding a whole range of the gravitational coupling constant k{sub 0} for which the functional integral is dominated by nondegenerate three-dimensional space-times.
Crossing the c=1 barrier in 2d Lorentzian quantum gravity
TLDR
Analysis of a system of eight Ising models coupled to dynamically triangulated Lorentzian geometries provides evidence for the conjecture that the KPZ values of the critical exponents in 2d Euclidean quantum gravity are entirely due to the presence of baby universes.
Scaling in four-dimensional quantum gravity
Simulations of Four-Dimensional Simplicial Quantum Gravity as Dynamical Triangulation
Four-Dimensional Simplicial Quantum Gravity is simulated using the dynamical triangulation approach. We studied simplicial manifolds of spherical topology and found the critical line for the
Quantum geometry with intrinsic local causality
The space of states and operators for a large class of background independent theories of quantum spacetime dynamics is defined. The SU(2) spin networks of quantum general relativity are replaced by
Integrable 2D Lorentzian gravity and random walks
Causal evolution of spin networks
Renormalization Group and Quantum Gravity
Scaling behavior of quantum four - geometries
...
...