The Witten Deformation of the Non-Minimal de Rham–Hodge Operator and Noncommutative Residue on Manifolds with Boundary
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 grav...
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2024-11-01
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| author | Tong Wu Yong Wang |
| author_facet | Tong Wu Yong Wang |
| author_sort | Tong Wu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-280fee499619404fbd4dcc542e653d9f |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj-art-280fee499619404fbd4dcc542e653d9f2024-11-26T18:11:43ZengMDPI AGMathematics2227-73902024-11-011222353010.3390/math12223530The Witten Deformation of the Non-Minimal de Rham–Hodge Operator and Noncommutative Residue on Manifolds with BoundaryTong Wu0Yong Wang1Department of Mathematics, Northeastern University, Shenyang 110819, ChinaSchool of Mathematics and Statistics, Northeast Normal University, Changchun 130024, ChinaUnder 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.https://www.mdpi.com/2227-7390/12/22/3530the Lichnerowicz type formulathe Witten deformationthe non-minimal de Rham–Hodge operatorthe Kastler–Kalau–Walze-type theorem |
| spellingShingle | Tong Wu Yong Wang The Witten Deformation of the Non-Minimal de Rham–Hodge Operator and Noncommutative Residue on Manifolds with Boundary Mathematics the Lichnerowicz type formula the Witten deformation the non-minimal de Rham–Hodge operator the Kastler–Kalau–Walze-type theorem |
| title | The Witten Deformation of the Non-Minimal de Rham–Hodge Operator and Noncommutative Residue on Manifolds with Boundary |
| title_full | The Witten Deformation of the Non-Minimal de Rham–Hodge Operator and Noncommutative Residue on Manifolds with Boundary |
| title_fullStr | The Witten Deformation of the Non-Minimal de Rham–Hodge Operator and Noncommutative Residue on Manifolds with Boundary |
| title_full_unstemmed | The Witten Deformation of the Non-Minimal de Rham–Hodge Operator and Noncommutative Residue on Manifolds with Boundary |
| title_short | The Witten Deformation of the Non-Minimal de Rham–Hodge Operator and Noncommutative Residue on Manifolds with Boundary |
| title_sort | witten deformation of the non minimal de rham hodge operator and noncommutative residue on manifolds with boundary |
| topic | the Lichnerowicz type formula the Witten deformation the non-minimal de Rham–Hodge operator the Kastler–Kalau–Walze-type theorem |
| url | https://www.mdpi.com/2227-7390/12/22/3530 |
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