Geodesic
Quantization on supermanifolds and an analytic proof of the Atiyah–Singer index theorem
Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Itogi Nauki i Tekhniki. Seriya "Sovremennye Problemy Matematiki. Noveishie Dostizheniya", Tome 38 (1990), pp. 3-118
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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. 
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     author = {F. F. Voronov},
     title = {Quantization on supermanifolds and an analytic proof of the {Atiyah{\textendash}Singer} index theorem},
     journal = {Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya},
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     volume = {38},
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F. F. Voronov. Quantization on supermanifolds and an analytic proof of the Atiyah–Singer index theorem. Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Itogi Nauki i Tekhniki. Seriya "Sovremennye Problemy Matematiki. Noveishie Dostizheniya", Tome 38 (1990), pp. 3-118. http://geodesic.mathdoc.fr/item/INTD_1990_38_a0/