The Spectral Action, Heat Coefficients and Loop Quantum Gravity

LQP 36 Foundations and Constructive Aspects of Quantum Field Theory
Christoph Stephan on May 30, 2015

In this talk I will consider closed Riemannian manifolds equipped with orthogonal connections (with torsion). I will review Einstein-Cartan-Hilbert theory and the Holst action which are starting points for Loop Quantum Gravity. Next, I will consider Dirac operators which are induced by orthogonal connections. Connes’ spectral action principle states that all physically relevant actions should be deducible from the spectrum of a suitable Dirac operator. The construction of the spectral action builds on the knowledge of the Seeley-deWitt coefficients obtained from an asymptotic expansion of the heat trace. I will present a formula for the spectral action in the presence of torsion, discuss its critical points and describe a possible connection to Loop Quantum Gravity. This project is joint work with Frank Pfäffle.