Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 3 (2007), 098, 29 pages      arXiv:0708.1705      https://doi.org/10.3842/SIGMA.2007.098
Contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson

Quantum Gravity: Unification of Principles and Interactions, and Promises of Spectral Geometry

Bernhelm Booß-Bavnbek a, Giampiero Esposito b and Matthias Lesch c
a) IMFUFA, Roskilde University, P.O. Box 260, 4000 Roskilde, Denmark
b) INFN, Sezione di Napoli and Dipartimento di Scienze Fisiche, Complesso Universitario di Monte S. Angelo, Via Cintia, Edificio 6, 80126 Napoli, Italy
c) Bonn University, Mathematical Institute, Beringstr. 6, D-53115 Bonn, Germany

Received August 14, 2007, in final form September 25, 2007; Published online October 05, 2007

Abstract
Quantum gravity was born as that branch of modern theoretical physics that tries to unify its guiding principles, i.e., quantum mechanics and general relativity. Nowadays it is providing new insight into the unification of all fundamental interactions, while giving rise to new developments in modern mathematics. It is however unclear whether it will ever become a falsifiable physical theory, since it deals with Planck-scale physics. Reviewing a wide range of spectral geometry from index theory to spectral triples, we hope to dismiss the general opinion that the mere mathematical complexity of the unification programme will obstruct that programme.

Key words: general relativity; quantum mechanics; quantum gravity; spectral geometry.

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