Spectral forms and de-Rham Hodge operator

Abstract

Motivated by the trilinear functional of differential one-forms, spectral triple and spectral torsion for the Hodge-Dirac operator, we introduce a multilinear functional of differential one-forms for a finitely summable regular spectral triple with a noncommutative residue, which generalize the spectral torsion defined by Dabrowski-Sitarz-Zalecki. The main results of this paper recover two forms, torsion of the linear connection and four forms by the noncommutative residue and perturbed de-Rham Hodge operators, and provides an explicit computation of generalized spectral torsion associated with the perturbed de-Rham Hodge Dirac triple.

arXiv admin note: text overlap with arXiv:2408.07149

References in corpus (9)

• Differential Forms and the Wodzicki Residue for Manifolds with Boundary
• Gravity and the Noncommutative Residue for Manifolds with Boundary
• Quantum Gravity Boundary Terms from Spectral Action of Noncommutative Space
• Dynamic critical behavior of the worm algorithm for the Ising model
• Ab Initio Study of 40Ca with an Importance Truncated No-Core Shell Model
• A superfluid helium converter for accumulation and extraction of ultracold neutrons
• Spectral Metric and Einstein Functionals
• Spectral Torsion
• A Kastler-Kalau-Walze type theorem for the J-twist D_J of the Dirac operator