The Witten Deformation of the Non-Minimal de Rham–Hodge Operator and Noncommutative Residue on Manifolds with Boundary
| Autor: | Tong Wu, Yong Wang |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Mathematics, Vol 12, Iss 22, p 3530 (2024) |
| Druh dokumentu: | article |
| ISSN: | 12223530 2227-7390 |
| DOI: | 10.3390/math12223530 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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