Discrete and continuum third quantization of Gravity

Understand

We give a brief introduction to matrix models and the group field theory (GFT) formalism as realizations of the idea of a third quantization of gravity, and present in some more detail the idea and basic features of a continuum third quantization formalism in terms of a field theory on the space of connections, building up on the results of loop quantum gravity that allow to make the idea slightly more concrete.

• We explore to what extent one can rigorously define such a field theory.
• Concrete examples are given for the simple case of Riemannian GR in 3 spacetime dimensions.
• We discuss the relation between GFT and this formal continuum third quantized gravity, and what it can teach us about the continuum limit of GFTs.