AG Mathematische Physik, Thomas Thiemann (FAU Physik): On representations of the hypersurface deformation algebroid of quantum gravity

Thomas Thiemann (FAU Physik)

On representations of the hypersurface deformation algebroid of quantum gravity

Abstract:

Quantum Gravity (QG), understood as a Quantum Field Theory (QFT) of General Relativity (GR), faces mathematical challenges that go beyond those of QFT in curved spacetime (CST). In this talk we focus on the hypersurface deformation algebroid (HDA) which in the classical theory encodes the Einstein equations. Implementing the quantum dynamics leads to the analysis of representations thereof by operators in QG.
After an introduction to those concepts, we show that non-trivial representations of the HDA exist in a weak coupling limit of GR in 3+1 dimensions with
2 propagating, self-interacting polarisations.