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.
- Dirac operator
- Euclidean Schwarzschild space
- Euclidean Taub-NUT space
- spectrum of Laplace operator
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)