Trace and index of Dirac–Schrödinger operators on open space with operator potentials
Abstract
We develop a principal trace and generalized index formula for a Dirac–Schrödinger operator D on open space of odd dimension d\geq 3 with a potential given by a family of self-adjoint unbounded operators acting on an infinite-dimensional Hilbert space H . The presented results generalize formulas surrounding the Callias index theorem to the case of unbounded operator potentials, for which the operator D is not necessarily Fredholm. This is the principal novelty of this paper. As application, we include examples where the trace formula is used to calculate the Witten index of non-Fredholm massless (d+1) -Dirac–Schrödinger operators acting in L^{2} (\mathbb{R}^{d+1},H) .
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Numerical methods in inverse problems
Quantum Mechanics and Non-Hermitian Physics
Publication details
- Journal / source
- Journal of Spectral Theory
- Volume
- 16
- Issue
- 4
- Pages
- 1351–1428
- Publication date
- 24 June 2026
- Language
- EN