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AGPhil: Arbeitsgruppe Philosophie der Physik

AGPhil 16: Quantum Gravity 4

AGPhil 16.2: Talk

Thursday, March 21, 2024, 17:15–17:45, PTB SR AvHB

Simplicial Graviton from Selfdual Ashtekar Variables — •Wolfgang Wieland — University of Erlangen Nuremberg, Erlangen, Germany

Selfdual gravity is a reformulation of general relativity on the phase space of a SL(2,C) gauge theory. As pointed out by Abhay Ashtekar in the mid 1980ies, this reformulation uncovered a surprising simplicity of gravity. It was a well-known result at the time that the Hamiltonian of the theory is a sum of constraints generating hypersurface deformations. The surprise was that using selfdual variables, the constraints simplify in a very dramatic way. They assume the simplest possible polynomial form. In this talk, I lay out a new non-perturbative lattice approach for selfdual gravity with possible far-reaching consequences for quantum gravity. Three results will be discussed. First of all, I explain how to introduce a local kinematical phase space at the lattice sites. At each lattice site, a set of constraints is found that replace the generators of hypersurface deformations in the continuum. The second and most intriguing result is that the discretized constraints close under the Poisson bracket. The resulting reduced phase space describes the two radiative modes at the discretized level. As consistency check, I apply the construction to gravity in three-dimensions. In this way, the established spin-network representation of three-dimensional gravity is recovered from a local quantisation of space.

Keywords: quantum gravity; selfdual variables; Hamiltonian formulation of general relativity; canonical quantization of Eisntein's equations