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The Atiyah-Singer Index Theorem for a Family of Fractional Dirac Operators on Spin Geometry

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Abstract

The Atiyah-Singer index formula for Dirac operators acting on the space of spinors put across a kind of topological invariant (\(\hat{{A}}\) genus) of a closed spin manifold \({{\mathcal {M}}}\), hence offering a bridge between geometric and analytical aspects of the original spin manifold. In this study, we prove the index theorem for a family of fractional Dirac operators in particular for complex analytic coordinates.

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Acknowledgements

The author would like to thank the anonymous referee for useful and valuable suggestions.

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The author would like to thank Chiang Mai University for funding this research.

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  1. Quantum-Atom Optics Laboratory and Research Center for Quantum Technology, Faculty of Engineering, Chiang Mai University, Chiang Mai, 50200, Thailand

    Rami Ahmad El-Nabulsi

  2. Department of Physics and Materials Science, Chiang Mai University, Chiang Mai, Thailand

    Rami Ahmad El-Nabulsi

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  1. Rami Ahmad El-Nabulsi
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Correspondence to Rami Ahmad El-Nabulsi.

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El-Nabulsi, R.A. The Atiyah-Singer Index Theorem for a Family of Fractional Dirac Operators on Spin Geometry. Adv. Appl. Clifford Algebras 33, 27 (2023). https://doi.org/10.1007/s00006-023-01270-2

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