On Geometric Spectral Functionals
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917407606439936 |
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| author | Bochniak, Arkadiusz Dąbrowski, Ludwik Sitarz, Andrzej Zalecki, Paweł |
| author_facet | Bochniak, Arkadiusz Dąbrowski, Ludwik Sitarz, Andrzej Zalecki, Paweł |
| contents | We investigate spectral functionals associated with Dirac and Laplace-type differential operators on manifolds, defined via the Wodzicki residue, extending classical results for Dirac operators derived from the Levi-Civita connection to geometries with torsion. The local densities of these functionals recover fundamental geometric tensors, including the volume form, Riemannian metric, scalar curvature, Einstein tensor, and torsion tensor. Additionally, we introduce chiral spectral functionals using a grading operator, which yields novel spectral invariants. These constructions offer a richer spectral-geometric characterization of manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16642 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Geometric Spectral Functionals Bochniak, Arkadiusz Dąbrowski, Ludwik Sitarz, Andrzej Zalecki, Paweł Mathematical Physics General Relativity and Quantum Cosmology Differential Geometry Spectral Theory 58B34, 58J50, 46L87, 83C65 We investigate spectral functionals associated with Dirac and Laplace-type differential operators on manifolds, defined via the Wodzicki residue, extending classical results for Dirac operators derived from the Levi-Civita connection to geometries with torsion. The local densities of these functionals recover fundamental geometric tensors, including the volume form, Riemannian metric, scalar curvature, Einstein tensor, and torsion tensor. Additionally, we introduce chiral spectral functionals using a grading operator, which yields novel spectral invariants. These constructions offer a richer spectral-geometric characterization of manifolds. |
| title | On Geometric Spectral Functionals |
| topic | Mathematical Physics General Relativity and Quantum Cosmology Differential Geometry Spectral Theory 58B34, 58J50, 46L87, 83C65 |
| url | https://arxiv.org/abs/2505.16642 |