A Kastler-Kalau-Walze Type Theorem for 5-dimensional Manifolds with Boundary

Abstract

The Kastler-Kalau-Walze theorem, announced by Alain Connes, shows that the Wodzicki residue of the inverse square of the Dirac operator is proportional to the Einstein-Hilbert action of general relativity. In this paper, we prove a Kastler-Kalau-Walze type theorem for 5-dimensional manifolds with boundary.

arXiv commentarXiv admin note: text overlap with arXiv:1303.3713, arXiv:1404.2339

References in corpus (11)

• Gravity, Non-Commutative Geometry and the Wodzicki Residue
• Curvature of Multiply Warped Products
• Differential Forms and the Wodzicki Residue for Manifolds with Boundary
• Gravity and the Noncommutative Residue for Manifolds with Boundary
• A Note on the Wodzicki Residue
• Lower dimensional volumes and the Kastler-Kalau-Walze type theorem for Manifolds with Boundary
• A generalized Lichnerowicz formula, the Wodzicki Residue and Gravity
• Noncommutative geometry and lower dimensional volumes in Riemannian geometry
• Dirac Operators with Torsion and the Noncommutative Residue for Manifolds with Boundary
• Chiral Asymmetry and the Spectral Action
• Noncommutative Residue and sub-Dirac Operators for Foliations