Dirac operators coupled to vector potentials.

@article{Atiyah1984DiracOC,
  title={Dirac operators coupled to vector potentials.},
  author={Michael Francis Atiyah and Isadore M. Singer},
  journal={Proceedings of the National Academy of Sciences of the United States of America},
  year={1984},
  volume={81 8},
  pages={2597-600}
}
Characteristic classes for the index of the Dirac family [unk](A) are computed in terms of differential forms on the orbit space of vector potentials under gauge transformations. They represent obstructions to the existence of a covariant Dirac propagator. The first obstruction is related to a chiral anomaly. 
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