Konzeptionelle Fragen der Quantengravitation und mathematischer Strukturen in der dreidimensionalen Gravitation

• Antragstellerin: Professorin Dr. Catherine Meusburger
• Fachliche Zuordnung: Kern- und Elementarteilchenphysik, Quantenmechanik, Relativitätstheorie, Felder
• Förderung: Förderung von 2008 bis 2016
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 76859343

Gravity is the only one of the four fundamental interactions for which quantum theory could not be constructed so far. This is due to the presence of conceptual problems which cannot be addressed within existing quantisation approaches. This includes the construction of a quantum theory without relying on a fixed background spacetime - in quantum gravity it is time and space themselves that are to be quantised - the role of time in the quantum theory, the question if time and space are continuous or discrete and the emergence of gravity for low energies. While a full quantum theory of four-dimensional gravity is currently not within reach, 3d gravity (one space, two time dimensions) serves as a toy model which allows one to address these conceptual questions in a fully quantised theory and to gain insights relevant to higher dimensions. Moreover, 3d gravity is of high importance for mathematics. The theory ties together many areas of current research, which lead to major progress in the subject. The research project aims to address several important conceptual questions of 3d quantum gravity. Besides their importance to the research subject of quantum gravity, these questions are also highly relevant to mathematics. In particular, they involve and relate concepts and methods from the theory of quantum groups, moduli spaces of flat connections, hyperbolic geometry and topological quantum field theory.

• DFG-Verfahren: Emmy Noether-Nachwuchsgruppen