Spectral Properties of Schwarzschild Instantons

Abstract

We study spectral properties of the Dirac and scalar Laplace operator on the Euclidean Schwarzschild space, both twisted by a family of abelian connections with anti-self-dual curvature. We show that the zero-modes of the gauged Dirac operator, first studied by Pope, take a particularly simple form in terms of the radius of the Euclidean time orbits, and interpret them in the context of geometric models of matter. For the gauged Laplace operator, we study the spectrum of bound states numerically and observe that it can be approximated with remarkable accuracy by that of the exactly solvable gauged Laplace operator on the Euclidean Taub-NUT space.

26 pages, 2 figures, 2 tables

References in corpus (3)

• Dirac operators on the Taub-NUT space, monopoles and SU(2) representations
• Time evolution in a geometric model of a particle
• Taub-NUT Dynamics with a Magnetic Field

Cited by in corpus (7)

• Geodesic motion in Euclidean Schwarzschild geometry
• Geometric Models of Helium
• Harmonic Spinors on a Family of Einstein Manifolds
• Harmonic Forms and Spinors on the Taub-bolt Space
• Cartan Connections and Integrable Vortex Equations
• Magnetic Zero-Modes, Vortices and Cartan Geometry
• Spectral Geometry of Nuts and Bolts