Invitation to a talk: Wolfgang Wieland

New boundary variables for classical and quantum gravity

In loop quantum gravity, we have a pretty good understanding of the quantum geometry in the bulk. What is missing is a clear picture of what is going on at boundaries, in particular boundaries that are null, which seems to be the most relevant case physically. In my talk, I present a series of results on this frontier: At the classical level, I consider general relativity in terms of self-dual variables in domains with inner null boundaries. At these null boundaries, a new pair of canonical variables appears, which consists of a spinor and a conjugate spinor-valued two-form. Using these boundary spinors, I discuss some aspects of the quantum theory, in particular the quantisation of area. In fact, the area of a two-dimensional cross section has a discrete spectrum, and no spin-networks or SU(2) variables are ever required for deriving this result. Finally, I present a proposal for how to formulate the dynamics for discretised gravity in terms of these variables as topological field theory on a system of internal null boundaries.