A Kastler-Kalau-Walze type theorem and the spectral action for perturbations of Dirac operators on manifolds with boundary

Abstract

In this paper, we prove a Kastler-Kalau-Walze type theorem for perturbations of Dirac operators on compact manifolds with or without boundary. As a corollary, we give two kinds of operator-theoretic explanations of the gravitational action on boundary. We also compute the spectral action for Dirac operators with two-form perturbations on $4$-dimensional compact manifolds.

21 pages, to appear in ABSTR APPL ANAL

References in corpus (3)

• Gravity coupled with matter and foundation of non-commutative geometry
• The Spectral Action Principle
• Type III and spectral triples