Quantization on supermanifolds and an analytic proof of the Atiyah–Singer index theorem

An analytic proof of the Atiyah–Singer index, theorem is given with the help of the tools of supermathematics. The index formula for the Dirac operator on a spinor manifold is obtained here by direct calculation. A large portion of the paper is devoted to questions of quantization on supermanifolds, using spinors as example.