A Kastler-Kalau-Walze Type Theorem and the Spectral Action for Perturbations of Dirac Operators on Manifolds with Boundary

Abstract

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.