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arxiv: 2307.14877 · v3 · pith:J5DLTPZ7 · submitted 2023-07-27 · math.DG · math-ph· math.MP· math.QA· math.SP

Spectral Metric and Einstein Functionals for Hodge-Dirac operator

Ludwik D\k{a}browski , Pawe{\l} Zalecki , Andrzej Sitarz This is my paper

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keywords functionalsoperatoreinsteinhodge-diracmanifoldmetricspectralassociated
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We examine the metric and Einstein bilinear functionals of differential forms introduced in Adv.Math.,Vol.427,(2023)1091286, for Hodge-Dirac operator $d+\delta$ on an oriented even-dimensional Riemannian manifold. We show that they reproduce these functionals for the canonical Dirac operator on a spin manifold up to a numerical factor. Furthermore, we demonstrate that the associated spectral triple is spectrally closed, which implies that it is torsion-free.

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  1. On Geometric Spectral Functionals

    math-ph 2025-05 unverdicted novelty 6.0

    Spectral functionals via Wodzicki residue recover geometric tensors including volume, metric, curvature and torsion on manifolds with torsion and yield chiral invariants.