Dirac operators and local invariants on perturbations of Minkowski space

Nguyen Viet Dang; András Vasy; Michał Wrochna

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arXiv · 2412.12714

Dirac operators and local invariants on perturbations of Minkowski space

Nguyen Viet Dang·András Vasy·Michał Wrochna

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Abstract

For small perturbations of Minkowski space, we show that the square of the Lorentzian Dirac operator $P= -D^2$ has real spectrum apart from possible poles in a horizontal strip. Furthermore, for $\varepsilon>0$ we relate the poles of the spectral zeta function density of $P-i\varepsilon$ to local invariants, in particular to the Lorentzian scalar curvature. The proof involves microlocal propagation and radial estimates in a resolved scattering calculus as well as high energy estimates in a further resolved classical-semiclassical calculus.

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Nguyen Viet Dang, András Vasy, Michał Wrochna. 2024-12-17. Dirac operators and local invariants on perturbations of Minkowski space. https://arxiv.org/abs/2412.12714

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