3rd QGG Intensive Lectures: Spinfoam path integrals for Quantum Gravity

At the crossroads of several approaches to quantum gravity, Spinfoams propose a discrete path integral for quantum general relativity built from topological field theory. With the spectrum of geometric operators directly read from the representation theory of the local symmetry group, they can be interpreted as a quantized version of Regge calculus and can be understood as implementing the dynamics of quantum states geometry in loop quantum gravity. I will explain the basics of the formalism, the motivations, the mathematical framework and the main tools. In three space-time dimensions, the spinfoam quantization of 3d gravity is given by the Turaev-Viro topological invariant, which is intimately related to the quantization of Chern-Simons theory. I will explain in particular how the spinfoam amplitudes solve the Wheeler-de Witt equation, implement the invariance under 3d diffeomorphisms (despite being formulated in a discretized space-time) and lead to a quasi-local version of holography. In four space-time dimensions, general relativity can be formulated as an almost-topological theory and I will explain how the existing spinfoam models introduce a sea of topological defects to re-create the gravitational degrees of freedom from a topological path integral. Finally, I will show how spinfoams are naturally defined in terms of group field theory, which are generalized tensor models, and the prospects that this opens. I will conclude with the main challenges and open lines of research of the field.

Program:

July 26
10:00 - 10:15 Registration and reception
10:15 - 11:45 Lecture 1
11:45 - 13:30 Lunch & coffee break
13:30 - 15:00 Lecture 2
15:00 - 16:00 Coffee break
16:00 - 17:00 Lecture 3
17:10 - 18:30 Short talk session

July 27
10:00 - 11:45 Lecture 4
11:45 - 13:30 Lunch & coffee break
13:30 - 15:00 Lecture 5
15:00 - 16:00 Coffee break
16:00 - 17:00 Lecture 6
17:30 - 20:00 Banquet

July 28
10:00 - 11:45 Lecture 7
11:45 - 13:30 Lunch & coffee break
13:30 - 15:00 Lecture 8
15:00 - 16:00 Coffee break
16:00 - 17:30 Lecture 9 & Closing