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The Witten Deformation of the Non-Minimal de Rham–Hodge Operator and Noncommutative Residue on Manifolds with Boundary

Author

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  • Tong Wu

    (Department of Mathematics, Northeastern University, Shenyang 110819, China
    Key Laboratory of Data Analytics and Optimization for Smart Industry, Ministry of Education, Northeastern University, Shenyang 110819, China)

  • Yong Wang

    (School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China)

Abstract

Under the announcement by Alain Connes that the Wodzicki residue of the inverse square of the Dirac operator is proportional to the Einstein–Hilbert action of general relativity, we derive the Lichnerowicz-type formula for the Witten deformation of the non-minimal de Rham–Hodge operator and the gravitational action in the case of n-dimensional compact manifolds without boundary. Finally, we present the proof of the Kastler–Kalau–Walze-type theorem for the Witten deformation of the non-minimal de Rham–Hodge operator on four- and six-dimensional oriented compact manifolds with boundary.

Suggested Citation

  • Tong Wu & Yong Wang, 2024. "The Witten Deformation of the Non-Minimal de Rham–Hodge Operator and Noncommutative Residue on Manifolds with Boundary," Mathematics, MDPI, vol. 12(22), pages 1-23, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:22:p:3530-:d:1519247
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    References listed on IDEAS

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    1. Sining Wei & Yong Wang, 2020. "Modified Novikov Operators and the Kastler-Kalau-Walze-Type Theorem for Manifolds with Boundary," Advances in Mathematical Physics, Hindawi, vol. 2020, pages 1-28, March.
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