Seminar: The Dirac Operator: An Origin Story
Speaker: Jesus Sanchez, Clayton State University
Abstract: The Dirac operator, originally discovered by P. Dirac to unify a quantum description of the electron with Einstein’s Special Relativity, was rediscovered by M.F. Atiyah and I.M. Singer in their celebrated Atiyah-Singer index theorem. Rather surprisingly, neither P. Dirac nor Atiyah-Singer had insight as to where this operator may have originated from, the explanation for the Dirac operator had to wait for the arrival of supersymmetry. We derive the Dirac operator from this perspective, explaining the symplectic geometry contained within this construction of the Dirac operator, and explore its implications.
Host: Yanli Song