A unified geometric framework for boundary charges and dressings

Tuesday, Oct 23rd

Aldo Riello, Perimeter Institute
Title: A unified geometric framework for boundary charges and dressings 
PDF of the talk (2M)
Audio+Slides of the talk (41M)

By Jorge Pullin, LSU (with some help from Aldo)

The electromagnetic force and all the subatomic interactions are described by a class of theories known as “gauge theories”. Even gravitation, in its modern formulation due to Einstein, is a gauge theory of sorts, although a more complicated one. The mathematical formulation of these theories is characterized by peculiar redundancies, as if the simplest way to describe the system is through a plethora of different descriptions rather than through a single “true” one. This is most often seen as a mathematical quirk rather than as a hint of some deep property of nature. This talk explores the latter possibility and build on the idea that the rationale for gauge theories must be found not so much in some property of a single system taken in isolation, but rather in the way systems can come together and talk to each other. The first hint of this can be found in the fact that the natural objects populating a gauge theory (“observables”) are intrinsically nonlocal and therefore can’t be easily localized in a given region, without carefully keeping track of what happens at its boundaries. The simplest example of this phenomenon can be found in the electron, that can never be separated from its electric field, which in turn can be detected even at a distance from the electron. This talk presents a novel mathematical framework that by embracing the relational perspective unifies many seemingly unrelated aspects of gauge theories and might – in its future developments – clarifies the analogous but harder conceptual issues one finds on their way to quantum gravity.

Quantum extension of black holes

Tuesday, Oct 9th

Javier Olmedo, LSU
Title: Quantum Extension of Kruskal Black Holes 
PDF of the talk (500k)
Audio+Slides of the talk (17M)

By Jorge Pullin, LSU

In the interior of black holes the coordinates t and r swap roles. As one falls "towards the center" one is actually moving forward in time. This makes the interior of a black hole look like a contracting cosmology of a particular type, known as Kantowski-Sachs cosmology. This has allowed the use of loop quantum cosmology techniques to treat the interior of black holes. There have been several discussions of this, but they have some shortcomings. To begin with, they only cover the interior of the black hole. Moreover, some of the proposals have physical quantities with undesirable dependences on fiducial elements introduced in order to quantize or on the mass of the space-time.

This talk discusses overcoming these problems. To begin with, it is shown that the quantum treatment eliminates the singularity inside black holes and replaces with a region of large curvature. The value of the maximum curvature is universal and independent on the mass of the space-time. Moreover, it gives the same mass for the black hole to the past and to the future (unlike other treatments). In addition, the quantum theory is extended to the exterior region of the black hole. In the future it is expected to extend these ideas to other type of black hole space-times, like those with charge, spin and cosmological constant.

Computing volumes in spin foams

Tuesday, Sep 25th

Benjamin Bahr, DESY
Title: 4-volume in spin foam models from knotted boundary graphs 
PDF of the talk (3M)
Audio+Slides of the talk (15M)

by Jorge Pullin, LSU

There is an approach to quantum mechanics known as the path integral approach. In it, one considers all possible classical trajectories, not only the ones satisfying the equations of motion and assigns probabilities to each of them using a formula. The probabilities are summed and that gives the quantum probability to go from an initial state to a final state. In loop quantum gravity the initial and final states are given by spin networks, which are graphs with intersections and "colors" (a number) assigned to each edge. The trajectories connecting initial and final states therefore resemble a "foam" and are given the names of spin foams.

In this talk it was shown how to compute volumes of polytopes (regions of space-time bounded by flat sides, a generalization to higher dimensions of polyhedra of 3d) in spin foam quantum gravity. The calculation has nice connections with knot theory, the branch of math that studies how curves entangle with each other.

One of the central elements of spin foams is the formula that assigns the probabilities, known as a "vertex". The construction in this talk gives ideas for extending the current candidates for vertices, including the possibility of adding a cosmological constant and suggests possible connections with Chern-Simons theories (a special type of field theories) and also with quantum groups.