Lorentzian Spectral Geometry for Globally Hyperbolic Surfaces

Abstract

The fermionic signature operator is analyzed on globally hyperbolic Lorentzian surfaces. The connection between the spectrum of the fermionic signature operator and geometric properties of the surface is studied. The findings are illustrated by simple examples and counterexamples.

49 pages, LaTeX, 7 figures, minor improvements (published version)

Cited by in corpus (8)

• The Fermionic Projector in a Time-Dependent External Potential: Mass Oscillation Property and Hadamard States
• Causal Fermion Systems: A Primer for Lorentzian Geometers
• Black Hole singularity and its possible mitigations: Reformulation of Penrose Singularity theorem using null Raychaudhuri matrix
• A skeletal model for 2d conformal AQFTs
• Lorentzian Spectral Geometry with Causal Sets
• The Fermionic Signature Operator in the Exterior Schwarzschild Geometry
• The Fermionic Signature Operator and Hadamard States in the Presence of a Plane Electromagnetic Wave
• A Canonical Complex Structure and the Bosonic Signature Operator for Scalar Fields in Globally Hyperbolic Spacetimes