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The representation ambiguity in loop quantum gravity

Wednesday 9th November 2005 - 11:00 to 12:30
INI Seminar Room 2

One of the main achievements of loop quantum gravity is the consistent quantization of the analog of the Wheeler-DeWitt equation which is free of ultra-violet divergences. However, ambiguities associated to the intermediate regularization procedure lead to an apparently infinite set of possible theories. The absence of an UV problem---the existence of well behaved regularization of the constraints---is intimatelly linked with the ambiguities arising in the quantum theory. Among these ambiguities there is the one associated to the $SU(2)$ unitary representation used in the diffeomorphism covariant ``point-splitting'' regularization of the non linear functionals of the connection. This ambiguity is labelled by a half-integer $m$ and, here, it is referred to as the {\em $m$-ambiguity}. I will ellaborate on this issue and show some results that suggest that the degree of ambiguity is reduced when considering the dynamics in the corresponding theory.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons