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 (det e) 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.
  Go to previous page Go up Go to next page