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Résumé:

I'll give a critical review of the present status and recent progress of loop and spin foam approaches to quantization of four-dimensional general relativity, and raise various issues which challenge some of the methods and the results in these domains. In particular, I'll argue that there are indications that the present realization of the loop quantization provided by LQG might be anomalous, whereas the quantization strategy employed in the most of spin foam models is inconsistent with the rules of canonical quantization. On the other hand, I'll suggest modifications of these two approaches which may overcome their problems.