Peter Schupp: Gravity as free fall in graded geometry - RQI Circuit Bremen 2023

Title: Gravity as free fall in graded geometry
Abstract: Deformations of the algebra of quantum operators lead to a description of fundamental interactions that generalizes and in a sense unifies the principles of gauge theory and the geometric description of gravity as free fall in curved spacetime. This approach is already quite well established for electromagnetism and is for example useful for the description of charged particles in a magnetic monopole background. We shall show that also gravitational interactions find such an algebraic description, but the construction requires a graded (super) geometry setting. The construction suggests a novel somewhat more algebraic interpretation of key ingredients of general relativity. A practical motivation for this line of research is to make methods and results from gauge theory available for gravitational physics. Potential applications include Aharanov-Bohm type (geometric phase) effects for gravitational fields.
Talk delivered at ZARM on November 24th 2023.
Broadcast and editing by Rick Perche.