Spinors on Singular Spaces and the Topology of Causal Fermion Systems

Abstract

Causal fermion systems and Riemannian fermion systems are proposed as a framework for describing non-smooth geometries. In particular, this framework provides a setting for spinors on singular spaces. The underlying topological structures are introduced and analyzed. The connection to the spin condition in differential topology is worked out. The constructions are illustrated by many simple examples like the Euclidean plane, the two-dimensional Minkowski space, a conical singularity, a lattice system as well as the curvature singularity of the Schwarzschild space-time. As further examples, it is shown how complex and Kähler structures can be encoded in Riemannian fermion systems.

70 pages, LaTeX, 3 figures, small corrections and improvements (published version)

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Cited by in corpus (8)

• Causal Fermion Systems: An Elementary Introduction to Physical Ideas and Mathematical Concepts
• A Gauge Fixing Procedure for Causal Fermion Systems
• Modified Measures as an Effective Theory for Causal Fermion Systems
• The Chiral Index of the Fermionic Signature Operator
• Baryogenesis in Minkowski Spacetime
• The Fermionic Signature Operator in the Exterior Schwarzschild Geometry
• Notions of Fermionic Entropies of a Causal Fermion System
• Local spin base invariance from a global differential-geometrical point of view