On Geometric Spectral Functionals
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.
Authors
- Ludwik Dąbrowski (ORCID: https://orcid.org/0000-0001-7160-4555)
- Andrzej Sitarz (ORCID: https://orcid.org/0000-0003-1612-3761)
- Arkadiusz Bochniak (ORCID: https://orcid.org/0000-0001-7856-0452)
- Paweł Zalecki (ORCID: https://orcid.org/0000-0002-6401-1273)
Institutions
- Jagiellonian University (PL)
- Scuola Internazionale Superiore di Studi Avanzati (IT)
- Max Planck Institute of Quantum Optics (DE)
Publication Details
- Journal
- Symmetry Integrability and Geometry Methods and Applications
- Published
- 2026-04-14
- DOI
- https://doi.org/10.3842/sigma.2026.035
- Primary Topic
- Geometric Analysis and Curvature Flows
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Alexander von Humboldt-Stiftung
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- Deutsche Forschungsgemeinschaft
- Gruppo Nazionale per la Fisica Matematica