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."