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arXiv · 2504.02336

Spectral asymmetry via pseudodifferential projections: the massless Dirac operator

Matteo Capoferri·Beatrice Costeri·Claudio Dappiaggi
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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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Matteo Capoferri, Beatrice Costeri, Claudio Dappiaggi. 2025-04-03. Spectral asymmetry via pseudodifferential projections: the massless Dirac operator. https://doi.org/10.1007/s13324-026-01210-w

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