Index theorem and applications, a gentle review

DOI: 10.5176/2251-1911_CMCGS18.2

Authors: Philippe Durand, Dariush GHORBANZADEH, Luan Jaupi

Abstract: AThe theorem of the index of Atiyah and Singer revolutionized not only modern mathematics but also physics. It provides a theoretical framework for defining the supersymmetry, not yet discovered, concept in quantum field theory. The theory of geometric fields on a macroscopic scale becomes topological at the Planck scale. We owe it all to the theorem of the Atiyah- Singer index.

Keywords:index theorem, supersymmetry, heat kernel, K-theory.