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ISRN Mathematical Physics
Volume 2013 (2013), Article ID 509316, 17 pages
http://dx.doi.org/10.1155/2013/509316
Review Article

Conceptual Problems in Quantum Gravity and Quantum Cosmology

Institute for Theoretical Physics, University of Cologne, Zülpicher Strasse 77, 50937 Köln, Germany

Received 26 May 2013; Accepted 28 June 2013

Academic Editors: M. Montesinos and M. Sebawe Abdalla

Copyright © 2013 Claus Kiefer. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The search for a consistent and empirically established quantum theory of gravity is among the biggest open problems of fundamental physics. The obstacles are of formal and of conceptual nature. Here, I address the main conceptual problems, discuss their present status, and outline further directions of research. For this purpose, the main current approaches to quantum gravity are briefly reviewed and compared.