Spectral asymmetry via pseudodifferential projections: the massless Dirac operator

2025/04/03 by Capoferri, Matteo, Costeri, Beatrice, Dappiaggi, Claudio
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2504.02336

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.

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