Critical Overview of Loops and Foams

Understand

This is a review of the present status of loop and spin foam approaches to quantization of four-dimensional general relativity.

• It aims at raising various issues which seem to challenge some of the methods and the results often taken as granted in these domains.
• A particular emphasis is given to the issue of diffeomorphism and local Lorentz symmetries at the quantum level and to the discussion of new spin foam models.
• We also describe modifications of these two approaches which may overcome their problems and speculate on other promising research directions.