Title: On Visualizing Kaluza Klein and other Hidden Geometries Inside Gauge Theories (slides)

Speaker: Mario Serna (USAF)

Time: 14:00-14:35 (GMT+0), 2021.08.03

Abstract:

Geometric curvature is defined by dragging a vector in a parallel manner along a closed path and then identifying the curvature as proportional to the angle change after transport around the loop. This is the curvature used in General Relativity. This talk

will visually connect this concept of curvature to several approaches to manifest curvature in gauge theories in the context of electromagnetism. We will describe how to make rigorous the ‘rings’ used to depict Kaluza-Klein theory and how they relate to a Grassmanian’s approach described by Michael Atiyah and another approach from Ken Johnson that shows a hidden spatial geometry inside traditional gauge theories.