Work

On Geometric Spectral Functionals

Year: 2026

Type: article

Abstract: 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.

Source: Symmetry Integrability and Geometry Methods and Applications

DOI: 10.3842/sigma.2026.035

Authors: Arkadiusz Bochniak, Ludwik Dąbrowski, Andrzej Sitarz, Paweł Zalecki

Institutions: Max Planck Society, Max Planck Institute of Quantum Optics, Scuola Internazionale Superiore di Studi Avanzati, Jagiellonian University

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond