Ulm 2004 – wissenschaftliches Programm

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MP: Theoretische und Mathematische Grundlagen der Physik

MP I: HV I

MP I.1: Hauptvortrag

Montag, 15. März 2004, 16:30–17:20, H 22

Loop Quantum Gravity: Progress and Pitfalls — •Christian Fleischhack — Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstr. 22–26, 04103 Leipzig

During the last decade, loop quantum gravity has lead to many new and deep insights into quantum geometry, black hole physics and even quantum cosmology. It is very remarkable that this has been achieved using rigorous mathematical methods. Nevertheless, all that progress above depends crucially on two assumptions: the structure group is compact and the loops considered are piecewise analytic. In this talk, we are first going to study why these assumptions may be unsatisfactory from a physical point of view. Next, we will show that, however, a direct, naive extension of loop quantum gravity to noncompact structure groups or nonanalytic paths leads immediately to severe mathematical difficulties, often even inconsistencies. Stating some simple, but striking examples, we will discuss whether these issues have technical reasons or even might be of conceptual origin.