Supersymmetry and the Atiyah–Singer index theorem. I. Peierls brackets, Green’s functions, and a proof of the index theorem via Gaussian superdeterminants

Abstract

The Peierls bracket quantization scheme is applied to the supersymmetric system corresponding to the twisted spin index theorem. A detailed study of the quantum system is presented, and the Feynman propagator is exactly computed. The Green’s function and functional integral methods provide a direct derivation of the index as a single universal superdeterminant.