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

SIGMA
 Pub Date:
 October 2007
 DOI:
 10.3842/SIGMA.2007.098
 arXiv:
 arXiv:0708.1705
 Bibcode:
 2007SIGMA...3..098B
 Keywords:

 general relativity;
 quantum mechanics;
 quantum gravity;
 spectral geometry;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 Mathematical Physics
 EPrint:
 This is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/