Quantization of the volume of the simplest grain of space

Tuesday, October 19th

Hal Haggard, Bard College

Quantization of the Volume of the Simplest Grain of Space
PDF and Keynote of the talk (6M)
Audio+Slides of the talk (542M)
SRT (Subtitles) of the talk (80k)

By Jorge Pullin, LSU

There exists a concept in mathematics called "asymptotic resurgence" in which an infinite sum of terms exhibits a surprising behavior. The terms that appear late in the summation around one physically relevant point are exactly the same as the terms that appear early in the sum around another physically relevant point. The result is a rich connection between the physics at the two different extremes and has applications in many areas of physics, for instance in the calculations of intensities of rainbows.

This talk applies these ideas to the calculation of the volume in loop quantum gravity. The volume of a region of space is discrete in that theory and has a complicated expression depending on the details of the quantum state one is considering. The expressions are known but are difficult to interpret. Previous studies have dealt with them primarily through numerical methods. In this talk an approximate expression is derived that can be much more easily interpreted and studied. It applies it to the simplest "grain" of space, a tetrahedron. A neat illustration of the power of the insights that can be learned from having an easier to interpret expression is the following movie following tetrahedra of different shape but equal volume:

To quote the concluding slide: "Quantization of geometry provides a remarkable laboratory for understanding resurgent perturbative/non-perturbative relations and, due to the richness of its underlying quantum structure, may even require extensions of this formalism."

Complex critical points and curved geometries in Lorentzian EPRL spinfoam amplitude

 Tuesday, October 5th

Dongxue Qu, Florida Atlantic University

Complex critical points and curved geometries in Lorentzian EPRL spinfoam amplitude
PDF of the talk (3M)
Audio+Slides of the talk (390M)
SRT (Subtitles) of the talk (80k)

By Jorge Pullin, LSU

The states of quantum gravity in the loop representation are given by spin networks. These are multivalent graphs with a number associated with each line. Spin foams represent the transition from an initial spin network state to a final one, as show in the figure (credit: Alejandro Perez). The expanded picture on the right is what is known as a "vertex", where new lines in the spin network are created as it transitions forward in time (time is the vertical axis). These diagrammatics correspond to precise mathematical 

equations that embody the dynamics of general relativity at a quantum level. One of the proposals for the vertex is the "EPRL" one (after Engle, Pereira, Rovelli and Livine). There has been controversy over the years about if the vertex correctly encoded the dynamics of general relativity. That requires studying how it behaves in the classical limit, as one expects departures from classical general relativity in situations where quantum effects are important. Previous calculations, done within certain approximations, seemed to suggest that curved geometries were not properly captured by this construction. The talk was about recent numerical results that imply that indeed it does capture the dynamics of classical general relativity in appropriate situations. Connections were made with a discretization of classical general relativity proposed by Tullio Regge known as Regge calculus. This is a very encouraging result indicating that the dynamics of classical general relativity is properly being captured by the "EPRL vertex".