Spectral asymmetry via pseudodifferential projections: the massless Dirac operator
Abstract
Abstract A new approach to the study of spectral asymmetry for systems of partial differential equations (PDEs) on closed manifolds was proposed in a recent series of papers by the first author and collaborator. They showed that information on spectral asymmetry can be encoded within and recovered from a negative order pseudodifferential operator — the asymmetry operator — constructed from appropriately defined pseudodifferential (spectral) projections. In this manuscript we apply these techniques to the study of the massless Dirac operator; in particular, we compute the principal symbol of the asymmetry operator, accounting for the underlying gauge invariance.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Algebraic and Geometric Analysis
Quantum Mechanics and Non-Hermitian Physics
Publication details
- Journal / source
- Analysis and Mathematical Physics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 16
- Issue
- 4
- Publication date
- 8 June 2026
- Language
- EN