This series consists of talks in the area of Quantum Gravity.
The covariant (spinfoam) formulation of loop gravity is a tentative physical quantum theory of gravity with well defined transition amplitudes. I give my current understanding of the state of the art in this research direction, the issues that are open and need to be explored, and the current attempts to use the theory to compute quantum effects in the early universe and in black hole physics.
It is well-known that quantum groups are relevant to describe the quantum regime of 3d gravity. They encode a deformation of the gauge symmetries (Lorentz symmetries) parametrized by the value of the cosmological constant. They appear as some kind of regularization either through the quantization of the Chern-Simons formulation (Fock-Rosly formulation/combinatorial quantization, path integral quantization) or the state sum approach (Turaev-Viro model). Such deformation might be perplexing from a classical picture since the action is defined in terms of plain/undeformed gauge symmetry.
In this talk I revisit the canonical framework for general relativity in its connection-frame field formulation, exploiting its local holographic nature. I will show how we can understand the Gauss law, the Bianchi identity and the space diffeomorphism constraints as conservation laws for local surface charges. These charges being respectively the electric flux, the dual magnetic flux and momentum charges. Quantization of the surface charge algebra can be done in terms of Kac-Moody edge modes.
Gauge theories possess nonlocal features that, in the presence of boundaries, inevitably lead to subtleties. In particular their fundamental degrees of freedom are not point-like. This leads to a non-trivial cutting (C) and sewing (S) problem:
(C) Which gauge invariant degrees of freedom are associated to a region with boundaries?
Quantizing 4D geometries leads to discrete area spectra. Such discrete area spectra are also suggested by the holographic principle and entropy counting for black holes.
In order to solve the problem of time in quantum gravity, various approaches to a relational quantum dynamics have been proposed. In this talk, I will exploit quantum reduction maps to illustrate a previously unknown equivalence between three of the well-known ones: (1) relational observables in the clock-neutral picture of Dirac quantization, (2) Page and Wootters’ (PW) Schrödinger picture formalism, and (3) the relational Heisenberg picture obtained via symmetry reduction. Constituting three faces of the same dynamics, we call this equivalence the trinity.
In this talk, we present a new outlook on canonical quantum gravity and its coupling to matter.
We will review the gravitational formula for fine grained entropy. We will discuss how it applies to an evaporating black hole and how we can compute the entropy of Hawking radiation.
In this talk I will discuss some recent results on boundary degrees of freedom (or edge modes), and their description via an extended phase space structure containing extra boundary fields. Motivated by a slight modification of the covariant phase space formalism, I will show how the use of a boundary Lagrangian enables to include the edge modes in the phase space and to obtain their boundary dynamics. This will be illustrated on the example of Maxwell theory, where in addition the edge modes can be understood as contributing to entanglement entropy.