2.9 Hamiltonian treatment. Introduction2 Gauge-theoretic discretizations of gravity2.7 Assorted topics

2.8 Summary

The gauge-theoretic Lagrangian lattice approaches are afflicted by a number of technical difficulties. Reflection positivity can be shown for some of the models, but generally requires the inclusion of a factor sign tex2html_wrap_inline2321 in the Lagrangian. Obtaining qualitative non-perturbative information about the phase structure requires a non-trivial measure input. The complicated functional form of the Lagrangian and the metricity condition that has to be imposed via a Lagrange multiplier and the corresponding functional integration do not make conformal and higher-derivative theories attractive candidates for numerical simulations. The compact version of Smolin's de Sitter gravity is still the simplest model, but its numerical investigation did not yield interesting results.

2.9 Hamiltonian treatment. Introduction2 Gauge-theoretic discretizations of gravity2.7 Assorted topics

image Discrete Approaches to Quantum Gravity in Four Dimensions
Renate Loll
http://www.livingreviews.org/lrr-1998-13
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