Quantum gravity: unification of principles and interactions, and promises of spectral geometry

Details Quantum gravity: unification of principles and interactions, and promises of spectral geometry Quantum gravity: unification of principles and interactions, and promises of spectral geometry

2007-08-13

arxiv.org/abs/0708.1705v3

SIGMA 3:098,2007

Physics

High Energy Physics

High Energy Physics - Theory

This is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson, published in

Scientific paper

10.3842/SIGMA.2007.098

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.

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